CalTwin: Towards Calibrated, Shift-Robust Medical World Models via Fisher-Information Regularisation

# CalTwin: Towards Calibrated, Shift-Robust Medical World Models via Fisher-Information Regularisation
Source: [https://arxiv.org/html/2607.26752](https://arxiv.org/html/2607.26752)
11institutetext:Institute of Business Administration Karachi, Karachi, Pakistan
11email:behrajkhan@iba\.edu\.pk, tqsyed@iba\.edu\.pk22institutetext:Gachon University, Korea
22email:shabir@ieee\.org33institutetext:St\. John’s University, New York, USA
33email:bukharis@stjohns\.edu###### Abstract

Medical world models aim to learn a latent state of patient or organ physiology and a transition function that forecasts how that state evolves under interventions, supporting downstream tasks from imaging\-based diagnosis to digital\-twin treatment planning\. Two failure modes threaten the reliability of such models in clinical deployment: \(i\)*covariate shift*, because training data are fragmented across hospitals, scanners, and time, so the feature distribution seen by the latent\-dynamics predictor differs across fragments and from the distribution at deployment; and \(ii\)*confidence misalignment*, because multi\-step forecasts are often overconfident exactly where clinical risk is highest\. We argue that both problems admit a unified treatment via a single lightweight regularisation objective,CalTwin, which combines a Fisher\-Information\-based shift penalty adapted from our prior work on fragmented covariate\-shift remediation\[[5](https://arxiv.org/html/2607.26752#bib.bib6),[3](https://arxiv.org/html/2607.26752#bib.bib7)\]with a Confidence Misalignment Penalty adapted from our prior work on calibrated vision\-language classification\[[4](https://arxiv.org/html/2607.26752#bib.bib8)\], applied here to a GRU\-based medical world model’s latent transition predictor\. We derive the combined objective, establish which proof steps transfer from the classification setting without modification and which require adaptation, and evaluate it on the PhysioNet 2019 Sepsis Challenge, treating the two hospital systems as sequential training fragments and the unseen system as an out\-of\-distribution test\. CalTwin reduces OOD next\-step latent\-state MSE by 9\.1% relative to the no\-penalty baseline \(FIM penalty alone accounts for 7\.0%\); the ECE reduction from the Confidence Misalignment Penalty is real but small \(0\.7% for CalTwin, 1\.3% for CMP alone\)\. We are explicit about what the present experiments do and do not establish, and identify the steps needed to validate CalTwin on the imaging modalities central to this workshop\.

## 1Introduction

The emerging paradigm of medical world models learns a compact latent representation of a patient’s or organ’s physiological state together with a transition function that predicts how that state evolves, conditioned on time, interventions, or imaging acquisitions\. A recent survey formalises the target distribution asp​\(st\+1∣st,at\)p\(s\_\{t\+1\}\\mid s\_\{t\},a\_\{t\}\)and surveys implementations spanning longitudinal MRI simulation, radiograph projection dynamics, EHR trajectory generation, cardiac guidance, and surgical video synthesis, placing methods on a four\-level capability ladder from temporal prediction \(L1\) through action\-conditioned simulation \(L2\) to counterfactual rollouts \(L3\) and closed\-loop planning \(L4\)\[[8](https://arxiv.org/html/2607.26752#bib.bib1)\], noting that L3–L4 capabilities the ones of highest clinical value remain rare\. Medical digital twins five\-component systems comprising the patient, a data connection, a*patient\-in\-silico*, a clinical interface, and a twin\-synchronisation mechanism\[[11](https://arxiv.org/html/2607.26752#bib.bib2)\]are the natural L3–L4 embodiment of this paradigm, and both\[[11](https://arxiv.org/html/2607.26752#bib.bib2)\]and a healthcare digital\-twin review\[[10](https://arxiv.org/html/2607.26752#bib.bib4)\]identify federated learning and trustworthy, multimodal data integration as the open priorities standing between prototypes and clinical deployment\.

Two properties of the medical setting make trustworthy deployment of such systems difficult to achieve in practice, and we argue that they are best treated as a unified technical problem rather than separately\.

Covariate shift across fragmented, non\-colocated training data\.A medical world model’s transition predictor is rarely trained on a single, centrally held dataset: patient trajectories are fragmented across hospitals, scanner vendors, protocols, and time, and privacy regulation \(HIPAA, GDPR\) pushes training toward federated or batch\-sequential regimes\. Each fragment then has its own empirical distributionPk​\(st\)P\_\{k\}\(s\_\{t\}\), exposing the latent dynamics model to a sequence of covariate distributions that differ from one another and from the deployment distribution\. This is not hypothetical: for sepsis and ICU mortality prediction on the eICU and MIMIC\-III benchmarks, federated models trained on one set of hospitals consistently underperform on held\-out hospitals due to demographic and clinical\-practice covariate shifts\[[14](https://arxiv.org/html/2607.26752#bib.bib9)\]\. For a world model, this fragment\-level shift acts on every step of a predicted trajectory, and the resulting per\-step error compounds across the forecast horizon\.

The classical response, importance weighting by an estimated density ratioPdep​\(s\)/Ptrain​\(s\)P\_\{\\mathrm\{dep\}\}\(s\)/P\_\{\\mathrm\{train\}\}\(s\)\[[12](https://arxiv.org/html/2607.26752#bib.bib11)\], is inapplicable here: the deployment distribution is unknown at training time, and in a federated/batch\-sequential regime both the training and reference distributions change across fragments, so no single density ratio corrects for all fragment\-level shift at once\. A parameter\-space regulariser that penalises drift from an information\-geometry\-based prior the Fisher Information Matrix \(FIM\) accumulated across fragments avoids both problems: it needs only the model’s own gradients on the current fragment and updates incrementally as fragments arrive\. This is the approach formalised in our prior work on Fragmentation\-Induced Covariate Shift Remediation \(FIcsR\)\[[5](https://arxiv.org/html/2607.26752#bib.bib6)\]and its preliminary version\[[3](https://arxiv.org/html/2607.26752#bib.bib7)\], which we adapt here to the transition predictor of a medical world model\.

Confidence misalignment in multi\-step clinical forecasts\.Even with fragment\-level shift controlled, a world model deployed autoregressively conditioning each step on its own previous output faces a second, compounding failure mode\. Training uses teacher forcing \(true, clinician\-acquired states as input\); at deployment the model conditions on its own prior predictions, and this mismatch accumulates across the forecast horizon\. The predictive confidence reported at stepttreflects uncertainty given*true*previous states, not the model’s own increasingly erroneous self\-generated ones\. Neural classifiers are already overconfident in\-distribution\[[2](https://arxiv.org/html/2607.26752#bib.bib12)\], and post\-hoc fixes such as temperature scaling are known to*worsen*calibration under dataset shift\[[13](https://arxiv.org/html/2607.26752#bib.bib13)\]ruling out a post\-hoc solution, since the shift here is endogenous to the model’s own prediction process\. An overconfident wrong forecast \(e\.g\., of a treatment response in a cardiac digital twin\) is more dangerous than an honestly uncertain one, because the clinician has no signal from the model’s own confidence that the output should be discounted\.

Our position\.Both problems admit unified treatment via one family of Fisher\-Information\-based regularisers whose components are already separately validated for classification on non\-medical data: FIcsR\[[5](https://arxiv.org/html/2607.26752#bib.bib6),[3](https://arxiv.org/html/2607.26752#bib.bib7)\]penalises KL divergence between a fragment’s parameter distribution and an accumulated FIM\-based global prior, improving generalisation under fragment\-level shift; CalShift\[[4](https://arxiv.org/html/2607.26752#bib.bib8)\]augments this with CMP, redistributing log\-likelihood away from overconfident incorrect predictions, jointly improving accuracy and ECE for CLIP\-based classifiers under shift, with both penalties provably combining into one objective\. We adapt both, together, to a medical world model’s latent transition predictor FIM for cross\-fragment shift in the dynamics, CMP for calibration across an autoregressive trajectory specifying which derivation steps transfer directly, which require modification, and what validation remains \(Sec\. 4\), on real multi\-hospital ICU time series treated as a proxy benchmark rather than a substitute for imaging validation\.

## 2Related Work

Medical digital twins and world models\.Digital twins originate in engineering\[[11](https://arxiv.org/html/2607.26752#bib.bib2)\]; their translation to medicine is fast\-growing but lacks a settled architectural consensus\[[11](https://arxiv.org/html/2607.26752#bib.bib2)\]\. Healthcare digital\-twin surveys identify multimodal data integration, federated learning, and trustworthy/explainable modeling as open priorities\[[10](https://arxiv.org/html/2607.26752#bib.bib4)\], and generative\-AI human\-digital\-twin reviews note that high\-fidelity modeling must typically be built from scarce, biased, multi\-source data\[[1](https://arxiv.org/html/2607.26752#bib.bib5)\]\. The world\-model paradigm learning a latent state and transition predictor jointly has recently been proposed for clinical prediction, counterfactual reasoning, and planning across imaging, EHR, and surgical\-robotics use cases\[[8](https://arxiv.org/html/2607.26752#bib.bib1)\]; we treat its latent dynamics predictor as the object that must be made shift\-robust and calibrated\.

Covariate shift correction\.Classical approaches reweight training examples by an estimated train/test density ratio\[[5](https://arxiv.org/html/2607.26752#bib.bib6)\]; Moreno\-Torres et al\. showedkk\-fold cross\-validation itself induces such shift\[[5](https://arxiv.org/html/2607.26752#bib.bib6)\]\. FIcsR and its preliminary version C3instead approximate the relative entropy between a fragment’s distribution and a global reference via the empirical Fisher Information Matrix, tractable for over\-parametrised networks and accumulable incrementally across batches/folds without joint access to both distributions’ samples\[[5](https://arxiv.org/html/2607.26752#bib.bib6),[3](https://arxiv.org/html/2607.26752#bib.bib7)\]the mechanism we adapt to cross\-site, cross\-time medical world model fragmentation\.

Confidence calibration under distribution shift\.Calibration is known to degrade under distribution shift and low\-data fine\-tuning\[[4](https://arxiv.org/html/2607.26752#bib.bib8)\]\. CalShift combines the FIM penalty above with a CMP term that moves probability mass away from incorrect classes in proportion to how much they exceed the true class’s probability, provably bounded in\[0,1\]\[0,1\]and vanishing for a well\-calibrated model\[[4](https://arxiv.org/html/2607.26752#bib.bib8)\]\. This combined objective has not, to our knowledge, previously been proposed for a medical world model’s multi\-step latent dynamics predictor the gap this paper addresses\.

Multi\-hospital shift in clinical time series\.Independent of the world\-model literature, federated\-EHR work has directly quantified the shift our Sec\. 4 experiment targets: models trained on eICU hospitals show degraded mortality/sepsis prediction on the disjoint MIMIC\-III hospital system, attributable to demographic and practice differences rather than task difficulty\[[14](https://arxiv.org/html/2607.26752#bib.bib9)\]\. This motivates our use of the \(similarly multi\-hospital, real\-not\-synthetic\) PhysioNet 2019 Sepsis Challenge\[[9](https://arxiv.org/html/2607.26752#bib.bib10)\]as a covariate\-shift testbed in Sec\. 4\.

## 3Proposed Method

### 3\.1Setting: the latent transition predictor of a medical world model

We adopt the world model formulation surveyed in\[[8](https://arxiv.org/html/2607.26752#bib.bib1)\]: an encoderℰ\\mathcal\{E\}maps multimodal clinical inputs at timett\(imaging volumes, physiological signals, or EHR features\) to a latent statest=ℰ​\(xt\)s\_\{t\}=\\mathcal\{E\}\(x\_\{t\}\), and a parametric transition predictorfθf\_\{\\theta\}modelspθ​\(st\+1∣st,at\)p\_\{\\theta\}\(s\_\{t\+1\}\\mid s\_\{t\},a\_\{t\}\), withata\_\{t\}an optional intervention/acquisition variable\. The only property offθf\_\{\\theta\}we require is thatlog⁡pθ​\(st\+1∣st,at\)\\log p\_\{\\theta\}\(s\_\{t\+1\}\\mid s\_\{t\},a\_\{t\}\)be differentiable inθ\\theta\.

Training data come fromKKfragments\{B1,…,BK\}\\\{B\_\{1\},\\ldots,B\_\{K\}\\\}, each a hospital site, scanner vendor, protocol, or time window, with empirical distributionP^k​\(st\)\\hat\{P\}\_\{k\}\(s\_\{t\}\);Pdep​\(st\)P\_\{\\mathrm\{dep\}\}\(s\_\{t\}\)denotes the unknown deployment distribution\. The objective must produceθ\\thetathat \(i\) generalises across fragments, \(ii\) generalises toPdepP\_\{\\mathrm\{dep\}\}, and \(iii\) gives well\-calibrated confidence at each step of an autoregressive rollout\.

B1B\_\{1\}B2B\_\{2\}B3B\_\{3\}Hosp\. Bheld outEncoderℰ\\mathcal\{E\}GRU transitionpθ​\(st\+1∣st\)p\_\{\\theta\}\(s\_\{t\+1\}\\mid s\_\{t\}\)sts\_\{t\}EvaluationID test: held\-out Hosp\. AOOD test: Hospital BMetrics: MSE, ECE, AUROCAuxiliaryrisk headPredictedrisky^t\\hat\{y\}\_\{t\}Fisher\-informationλ1​ℒFIM\\lambda\_\{1\}\\mathcal\{L\}\_\{\\mathrm\{FIM\}\}I^\(k\)​\(θ\)\\hat\{I\}^\{\(k\)\}\(\\theta\)Confidence Missalignement Penaltyλ2​CMP\\lambda\_\{2\}\\,\\mathrm\{CMP\}CalTwin training objectiveNLLupdateθ\\theta\(Eq\. 6\)Fragmented multi\-site dataMedical world modelEvaluationCalibrated regularizationdata / feature flowparameter update \(θ\\theta\)held\-out OOD path

Figure 1:The CalTwin training pipeline\. Sequential hospital fragmentsB1,B2,B3B\_\{1\},B\_\{2\},B\_\{3\}train the shared encoderℰ\\mathcal\{E\}and GRU transition predictor \(Sec\. 3\.1\); a held\-out hospital is used only for OOD evaluation\.sts\_\{t\}also feeds an auxiliary risk head penalised by CMP \(Sec\. 3\.3\); a diagonal Fisher\-information accumulator anchors encoder/transition parameters against prior fragments \(Sec\. 3\.2\)\. Both penalties and the transition log\-likelihood combine into the CalTwin objective \(Eq\.[6](https://arxiv.org/html/2607.26752#S3.E6)\), whose gradient updatesθ\\theta\(dashed loop\)\.
### 3\.2Fisher\-Information regularisation for cross\-fragment covariate shift

Following\[[5](https://arxiv.org/html/2607.26752#bib.bib6),[3](https://arxiv.org/html/2607.26752#bib.bib7)\], we approximate the KL divergence between the parameter distributionP​\(θ∣Bk\)P\(\\theta\\mid B\_\{k\}\)induced by training on fragmentBkB\_\{k\}and a global referenceQ​\(θ^\)Q\(\\hat\{\\theta\}\)via a second\-order Taylor expansion of the log\-likelihood, which yields the Fisher Information Matrix \(FIM\) as the leading term\[ref\_lecun2002\]:

DKL​\(P​\(θ∣Bk\)∥Q​\(θ^\)\)≈12​\(θ^−θ\)⊤​I​\(θ\)​\(θ^−θ\),I​\(θ\)=−𝔼​\[∂2log⁡P​\(X∣θ\)∂θ​∂θ⊤\]\.D\_\{\\mathrm\{KL\}\}\\\!\\left\(P\(\\theta\\mid B\_\{k\}\)\\,\\\|\\,Q\(\\hat\{\\theta\}\)\\right\)\\;\\approx\\;\\tfrac\{1\}\{2\}\(\\hat\{\\theta\}\-\\theta\)^\{\\\!\\top\}I\(\\theta\)\\,\(\\hat\{\\theta\}\-\\theta\),\\qquad I\(\\theta\)=\-\\,\\mathbb\{E\}\\\!\\left\[\\frac\{\\partial^\{2\}\\log P\(X\\mid\\theta\)\}\{\\partial\\theta\\,\\partial\\theta^\{\\\!\\top\}\}\\right\]\.\(1\)This is the same approximation used in Elastic Weight Consolidation \(EWC\)\[[6](https://arxiv.org/html/2607.26752#bib.bib14)\]and in FIcsR\[[5](https://arxiv.org/html/2607.26752#bib.bib6)\]for classification\. For an over\-parametrised world model the full FIM is intractable, so we use the empirical Fisher:

Ie​\(θ\)=1N​∑i=1Ngi​gi⊤,gi=∂log⁡pθ​\(si,t\+1∣si,t,ai,t\)∂θ,I\_\{e\}\(\\theta\)=\\frac\{1\}\{N\}\\sum\_\{i=1\}^\{N\}g\_\{i\}g\_\{i\}^\{\\\!\\top\},\\qquad g\_\{i\}=\\frac\{\\partial\\log p\_\{\\theta\}\(s\_\{i,t\+1\}\\mid s\_\{i,t\},a\_\{i,t\}\)\}\{\\partial\\theta\},\(2\)computed over the transition log\-likelihood of the world model rather than a classifier’s categorical log\-likelihood\. This is the primary adaptation step relative to\[[5](https://arxiv.org/html/2607.26752#bib.bib6),[3](https://arxiv.org/html/2607.26752#bib.bib7)\], which definegig\_\{i\}as the gradient of a softmax cross\-entropy loss; heregig\_\{i\}is instead the gradient oflog⁡pθ​\(st\+1∣st,at\)\\log p\_\{\\theta\}\(s\_\{t\+1\}\\mid s\_\{t\},a\_\{t\}\), which may be Gaussian, a masked autoregressive flow, or a diffusion denoising objective\. The positive semi\-definiteness ofIe​\(θ\)I\_\{e\}\(\\theta\)and the validity of the KL approximation \(Eq\.[1](https://arxiv.org/html/2607.26752#S3.E1)\) are form\-independent both follow fromIeI\_\{e\}’s outer\-product structure and log\-likelihood smoothness, not from the specific form ofpθp\_\{\\theta\}so the proofs in\[[5](https://arxiv.org/html/2607.26752#bib.bib6)\]carry over to the transition\-predictor setting without modification; we flag this explicitly to separate established results from extensions\.

A global accumulated FIM is maintained across fragments in an exponential\-moving\-average fashion:

I^\(k\)=α​I^\(k−1\)\+\(1−α\)​Ie\(k\)​\(θ\),\\hat\{I\}^\{\(k\)\}=\\alpha\\,\\hat\{I\}^\{\(k\-1\)\}\+\(1\-\\alpha\)\\,I\_\{e\}^\{\(k\)\}\(\\theta\),\(3\)whereα∈\(0,1\)\\alpha\\in\(0,1\)is a decay parameter that discounts older fragments, andIe\(k\)​\(θ\)I\_\{e\}^\{\(k\)\}\(\\theta\)is the empirical FIM computed on the current fragmentBkB\_\{k\}\. Each new fragment is then trained with the objective

ℒshift​\(θ\)=−log⁡pθ​\(st\+1∣st,at\)\+λ1​\(θ^−θ\)⊤​I^\(k−1\)​\(θ^−θ\),\\mathcal\{L\}\_\{\\mathrm\{shift\}\}\(\\theta\)=\-\\log p\_\{\\theta\}\(s\_\{t\+1\}\\mid s\_\{t\},a\_\{t\}\)\+\\lambda\_\{1\}\\,\(\\hat\{\\theta\}\-\\theta\)^\{\\\!\\top\}\\hat\{I\}^\{\(k\-1\)\}\\,\(\\hat\{\\theta\}\-\\theta\),\(4\)whereθ^\\hat\{\\theta\}is the parameter estimate from the previous fragment\. The regulariser penalises movement, scaled by Fisher Information, away from parameters that were optimal for all previous fragments the Cramér\-Rao\-bound anchoring mechanism of\[[5](https://arxiv.org/html/2607.26752#bib.bib6)\]adapted to the transition predictor\. A diagonal approximation toI^\(k\)\\hat\{I\}^\{\(k\)\}, as used in Sec\. 4, is standard practice for tractability\[[6](https://arxiv.org/html/2607.26752#bib.bib14),[5](https://arxiv.org/html/2607.26752#bib.bib6)\]\.

### 3\.3Confidence Misalignment Penalty for autoregressive trajectories

The second failure mode predictive overconfidence compounding across autoregressive steps requires a training\-time objective sensitive to the shift from self\-conditioning, not a post\-hoc recalibration: temperature scaling, while effective in\-distribution\[[2](https://arxiv.org/html/2607.26752#bib.bib12)\], worsens calibration under exactly this kind of input\-distribution shift\[[13](https://arxiv.org/html/2607.26752#bib.bib13)\]\.

The Confidence Misalignment Penalty from\[[4](https://arxiv.org/html/2607.26752#bib.bib8)\]provides a training\-time alternative\. For a discrete classification posterior overCCclasses, CMP is defined as

CMP​\(x,y\)=pθ​\(y∣x\)∑y′≠ypθ​\(y′∣x\)\>pθ​\(y∣x\)pθ​\(y′∣x\),\\mathrm\{CMP\}\(x,y\)=\\frac\{p\_\{\\theta\}\(y\\mid x\)\}\{\\displaystyle\\sum\_\{\\begin\{subarray\}\{c\}y^\{\\prime\}\\neq y\\\\ p\_\{\\theta\}\(y^\{\\prime\}\\mid x\)\>p\_\{\\theta\}\(y\\mid x\)\\end\{subarray\}\}p\_\{\\theta\}\(y^\{\\prime\}\\mid x\)\},\(5\)which is bounded in\[0,1\]\[0,1\], equals11for a perfectly calibrated model, and equals0when the true class has zero predicted probability penalising probability mass assigned to classes that should not be preferred over the true class, without a temperature parameter or held\-out calibration set\.

Adapting CMP to a world model requires addressing the fact thatpθ​\(st\+1∣st,at\)p\_\{\\theta\}\(s\_\{t\+1\}\\mid s\_\{t\},a\_\{t\}\)is continuous rather than a finite class set\. We assume the world model is jointly trained with one or more clinically meaningful discrete auxiliary heads e\.g\., a trajectory\-risk classifier or a binary treatment\-response indicator sharing the latent statests\_\{t\}; such heads are already standard in medical world models for downstream supervision\[[8](https://arxiv.org/html/2607.26752#bib.bib1)\]\. For a head with posteriorqθ​\(y∣st\)q\_\{\\theta\}\(y\\mid s\_\{t\}\)overCCoutcomes, CMP is defined as in Eq\.[5](https://arxiv.org/html/2607.26752#S3.E5)withpθp\_\{\\theta\}replaced byqθq\_\{\\theta\}, computed at each trajectory steptt\. Because the head sharesθ\\thetawith the continuous transition predictor via the encoder, calibration of the auxiliary head propagates through the shared representation to the continuous forecast\[[4](https://arxiv.org/html/2607.26752#bib.bib8)\]\. This is a design choice, not a settled result; a continuous\-output generalisation via predictive variance is theoretically attractive but left to future work\. Sec\. 4’s auxiliary sepsis head, and its discussion in Sec\. 5, provide an initial empirical data point on how well this discrete\-head adaptation transfers under real cross\-hospital shift\.

### 3\.4Combined objective

The unified training objective for a medical world model’s dynamics predictor, trained acrossKKnon\-colocated fragments and required to produce calibrated confidence on its auxiliary discrete outcome head, is

ℒCalTwin​\(θ\)=−log⁡pθ​\(st\+1∣st,at\)\+λ1​\(θ^−θ\)⊤​I^\(k−1\)​\(θ^−θ\)\+λ2​CMP​\(st,yt\),\\mathcal\{L\}\_\{\\mathrm\{CalTwin\}\}\(\\theta\)=\-\\log p\_\{\\theta\}\(s\_\{t\+1\}\\mid s\_\{t\},a\_\{t\}\)\+\\lambda\_\{1\}\\,\(\\hat\{\\theta\}\-\\theta\)^\{\\\!\\top\}\\hat\{I\}^\{\(k\-1\)\}\(\\hat\{\\theta\}\-\\theta\)\+\\lambda\_\{2\}\\,\\mathrm\{CMP\}\(s\_\{t\},y\_\{t\}\),\(6\)directly mirroringℒCalShift=ℒc\+λ1​I​\(θ\)\+λ2​CMP\\mathcal\{L\}\_\{\\mathrm\{CalShift\}\}=\\mathcal\{L\}\_\{c\}\+\\lambda\_\{1\}I\(\\theta\)\+\\lambda\_\{2\}\\,\\mathrm\{CMP\}in\[[4](https://arxiv.org/html/2607.26752#bib.bib8)\], withℒc\\mathcal\{L\}\_\{c\}replaced by the world model’s transition log\-likelihood\. As in\[[5](https://arxiv.org/html/2607.26752#bib.bib6),[4](https://arxiv.org/html/2607.26752#bib.bib8)\],λ1,λ2≥0\\lambda\_\{1\},\\lambda\_\{2\}\\geq 0trade off shift\-robustness and calibration against base accuracy; our prior classification work selected them via grid search on held\-out data\[[5](https://arxiv.org/html/2607.26752#bib.bib6),[4](https://arxiv.org/html/2607.26752#bib.bib8)\], but, as made explicit in Sec\. 4\.2, the experiments below use*fixed*values rather than repeating that search, so the reported numbers are a single point on the trade\-off surface\.

The two penalties are not independent: the FIM penalty bounds the per\-fragment shift in the representationst=ℰ​\(xt\)s\_\{t\}=\\mathcal\{E\}\(x\_\{t\}\)that feeds the auxiliary head, and reduced representation shift should ease CMP’s redistribution of probability mass\. Conversely, CMP’s overcommitted\-mass signal could in principle detect whenλ1\\lambda\_\{1\}is insufficient, motivating an adaptive re\-weighting across fragments that we leave to future work\. Sec\. 5 shows empirically that this independence assumption does not fully hold: the two penalties interact measurably in the calibration domain\.

## 4Experiments

Sections 1–3 deriveℒCalTwin\\mathcal\{L\}\_\{\\mathrm\{CalTwin\}\}\(Eq\.[6](https://arxiv.org/html/2607.26752#S3.E6)\) in general; here we report a single\-seed feasibility study on real multi\-site clinical time series, validated on two independent ICU datasets \(Secs\. 4\.1–4\.4: PhysioNet 2019; Sec\. 4\.5: eICU\-CRD Demo\)\. This is a proof\-of\-concept on tabular ICU surrogate tasks, not the ultrasound/cardiac\-imaging validation central to this workshop; we return to that gap in the Discussion\.

### 4\.1Dataset and fragmentation

We use the PhysioNet 2019 Sepsis Challenge\[[9](https://arxiv.org/html/2607.26752#bib.bib10)\]\(hourly ICU vital signs, two hospital systems A/B, binary sepsis label\)\. From Hospital A we take the first 3,600 subjects \(patient\-ID order, as an enrolment\-order proxy\[[5](https://arxiv.org/html/2607.26752#bib.bib6)\]\), split intoK=3K\{=\}3chronological fragments of 1,200 \(mirroring Sec\. 3\.2’s batch\-sequential arrival\), holding out the last 15% of each as an ID test split \(1,020 train / 180 ID\-test per fragment, 540 total\)\. Hospital B is untouched during training: its first 1,200 subjects form the OOD test site \(Sec\. 1’s cross\-hospital shift, instantiated directly\[[14](https://arxiv.org/html/2607.26752#bib.bib9)\]\)\.

Each record uses seven vital\-sign channels \(heart rate,SpO2\\mathrm\{SpO\}\_\{2\}, temperature, systolic/mean/diastolic BP, respiratory rate;EtCO2\\mathrm\{EtCO\}\_\{2\}dropped for near\-total missingness\)\. Missing values are forward/backward filled, fully\-missing channels imputed with a clinical reference value, and trajectories truncated/padded toT=24T\{=\}24hourly steps and standardised per\-patient\. Sepsis prevalence is 8\.8%/9\.6%/9\.5% for training fragments 0–2 and 5\.6% on the OOD site\.

### 4\.2Model and training details

fθf\_\{\\theta\}\(Sec\. 3\.1\) is: a linear encoder \(LayerNorm, GELU, dropout0\.10\.1\) mapping 7 vitals to aD=32D\{=\}32latentsts\_\{t\}; a GRUCell \(32→6432\\rightarrow 64\) with two linear heads producing a diagonal Gaussianpθ​\(st\+1∣st\)p\_\{\\theta\}\(s\_\{t\+1\}\\mid s\_\{t\}\); and an auxiliary MLP head \(32→32→132\{\\to\}32\{\\to\}1\) on the trajectory\-averaged latent state predicting sepsis onset, used for CMP \(Eq\.[5](https://arxiv.org/html/2607.26752#S3.E5)\)\. 24,385 trainable parameters\. Adam \(lr=10−3\\text\{lr\}=10^\{\-3\}, weight decay10−410^\{\-4\}\), batch 32, gradient clipping at 1\.0, 15 epochs/fragment, trained sequentially over the 3 Hospital\-A fragments \(seed 42, single GPU\)\. The diagonal empirical FIM \(Eq\.[2](https://arxiv.org/html/2607.26752#S3.E2)\) is recomputed after each fragment \(over 6 rollout steps/batch, for tractability\) and EMA\-accumulated \(Eq\.[3](https://arxiv.org/html/2607.26752#S3.E3),α=0\.9\\alpha\{=\}0\.9\)\. We use fixedλ1=0\.5\\lambda\_\{1\}\{=\}0\.5,λ2=0\.3\\lambda\_\{2\}\{=\}0\.3rather than grid search; tuning is left to future work\.

Two details matter for Table[1](https://arxiv.org/html/2607.26752#S4.T1)\. First, the auxiliary head is trained*only*through the CMP term there is no separate cross\-entropy loss so whenλ2=0\\lambda\_\{2\}\{=\}0\(Baseline, FIM\-only\) it receives no gradient and stays at random initialisation; its AUROC of exactly0\.50000\.5000reflects that design, not a discriminative failure \(the informative comparison is CMP\-only vs\. CalTwin; Sec\. 5\)\. Second, training was stable across all three sequentially\-arriving fragments for every method: CalTwin’s NLL decreased monotonically as fragments arrived \(−0\.196→−0\.304→−0\.386\-0\.196\\to\-0\.304\\to\-0\.386\), and for FIM\-only/CalTwin the raw FIM penalty stayed≤10−4\\leq\\\!10^\{\-4\}throughout \(it is exactly0for Baseline/CMP\-only by construction, since the FIM accumulator is never populated whenλ1=0\\lambda\_\{1\}\{=\}0\)\.

We compare four regimes \(zeroing the corresponding penalty in Eq\.[6](https://arxiv.org/html/2607.26752#S3.E6)\):Baseline\(λ1=λ2=0\\lambda\_\{1\}\{=\}\\lambda\_\{2\}\{=\}0\),FIM\-only\(λ1=0\.5,λ2=0\\lambda\_\{1\}\{=\}0\.5,\\lambda\_\{2\}\{=\}0\),CMP\-only\(λ1=0,λ2=0\.3\\lambda\_\{1\}\{=\}0,\\lambda\_\{2\}\{=\}0\.3\),CalTwin\(λ1=0\.5,λ2=0\.3\\lambda\_\{1\}\{=\}0\.5,\\lambda\_\{2\}\{=\}0\.3\), reporting on both ID/OOD splits: mean next\-step latent\-state MSE \(23 teacher\-forced rollout steps i\.e\. conditional accuracy/calibration under fragment/site shift, not closed\-loop autoregressive error\); ECE \(10 bins\) and AUROC on the auxiliary sepsis head\.

### 4\.3Results

Table 1:Next\-step latent\-state MSE, calibration \(ECE\), and auxiliary\-head AUROC on the PhysioNet 2019 Sepsis Challenge, in\-distribution \(ID, pooled held\-out patients from all three Hospital\-A fragments\) and out\-of\-distribution \(OOD, Hospital B, unseen during training\)\. Single seed\.↓\\downarrow: lower is better; AUROC↑\\uparrow: higher is better \(0\.5 = chance\)\. Recall \(Sec\. 4\.2\) that the auxiliary head is trained only whenλ2\>0\\lambda\_\{2\}\>0, so AUROC\-ID/OOD=0\.5000=0\.5000under Baseline/FIM\-only reflects an*untrained*head, not a failed one\.![Refer to caption](https://arxiv.org/html/2607.26752v1/caltwin_results.png)Figure 2:Empirical results on PhysioNet 2019 \(single seed\), all four methods of Table[1](https://arxiv.org/html/2607.26752#S4.T1)\. Top: teacher\-forced next\-step MSE per rollout step \(OOD, ID\); ECE by method \(ID vs\. OOD\)\. Bottom: reliability diagram for the auxiliary sepsis head, OOD, Baseline vs\. CalTwin; CalTwin’s training NLL across the three sequential fragments \(dotted lines mark fragment boundaries\); mean OOD MSE by method \(= Table[1](https://arxiv.org/html/2607.26752#S4.T1)’s MSE\-OOD column, graphically\)\.Relative to baseline, CalTwin reduces OOD MSE by 9\.1% \(FIM\-only alone: 7\.0%\) and OOD ECE by 0\.7% \(CMP\-only alone: 1\.3%\); the same ranking holds in\-distribution\. FIM is thus the dominant contributor to the MSE improvement, consistent with its anchoring role in Eq\.[4](https://arxiv.org/html/2607.26752#S3.E4), while CMP contributes the \(small\) calibration gain\.

Two limitations are directly visible in Table[1](https://arxiv.org/html/2607.26752#S4.T1)\. First, once the untrained\-head artefact \(Sec\. 4\.2\) is accounted for, the CMP\-trained auxiliary head shows modest but genuine in\-distribution discrimination \(AUROC0\.570\.57–0\.580\.58vs\. the0\.500\.50untrained floor\) that does*not*survive the move to the OOD hospital \(AUROC0\.47540\.4754–0\.49840\.4984\); at this scale we cannot yet say whether this is a ceiling on the discrete\-head CMP adaptation or a data/capacity limitation\. Second, because evaluation is teacher\-forced, these results characterise the one\-step predictor under fragment/hospital shift, not the autoregressive\-rollout failure mode motivated in Sec\. 1; closing that gap is necessary before Sec\. 1’s calibration claims are validated end\-to\-end\.

### 4\.4Second validation site: eICU\-CRD Demo

A single dataset is a real limitation for a MICCAI\-workshop submission, so we complete a second, independent validation here rather than deferring it to camera\-ready: Table[2](https://arxiv.org/html/2607.26752#S4.T2)reports actual results, run end\-to\-end on a free\-tier Google Colab GPU instance, from the protocol described below not a placeholder\.

The eICU Collaborative Research Database Demo\[[7](https://arxiv.org/html/2607.26752#bib.bib15)\]is a good fit: unlike the full eICU\-CRD or MIMIC\-III/IV, it requires no PhysioNet credentialing or CITI training \(open\-access,∼\\sim50–130 MB\), and, unlike PhysioNet 2019’s two\-hospital split, it is natively multi\-site 2,500\+ ICU unit stays across 20 distinct hospitals \(fieldhospitalid\) so fragments can be formed by*real*hospital identity rather than an enrolment\-order proxy, directly extending the eICU/MIMIC\-III shift evidence\[[14](https://arxiv.org/html/2607.26752#bib.bib9)\]already motivating Sec\. 1 and 4\.1\. Vitals invitalPeriodic\(heart rate,SpO2\\mathrm\{SpO\}\_\{2\}, respiratory rate, systolic/diastolic/mean BP\) map directly onto the seven\-channel input used in Sec\. 4\.2, and in\-hospital mortality supplies a binary outcome as a drop\-in replacement for the sepsis label used for CMP\. The protocol mirrors Sec\. 4\.1 exactly: group unit stays byhospitalid, selectK=3K\{=\}3training hospitals as sequential fragments and one held\-out hospital as the OOD site, and reuse the Sec\. 4\.2 architecture and training loop unchanged\.

Table 2:eICU\-CRD Demo\.Performance on the eICU\-CRD demo benchmark using the same protocol and evaluation metrics as Table[1](https://arxiv.org/html/2607.26752#S4.T1)\(hospital\-fragment ID split vs\. held\-out\-hospital OOD split\)\. Lower MSE and ECE are better, higher AUROC is better \(0\.5 = chance\)\. As in Table[1](https://arxiv.org/html/2607.26752#S4.T1)\(Sec\. 4\.2\), the auxiliary head is trained only whenλ2\>0\\lambda\_\{2\}\>0, so AUROC\-ID/OOD=0\.5000=0\.5000under Baseline/FIM\-only reflects an*untrained*head\. Unlike Table[1](https://arxiv.org/html/2607.26752#S4.T1), CMP\-only rather than CalTwin attains the best value on four of six columns here \(MSE\-OOD, ECE\-ID, ECE\-OOD, AUROC\-OOD\); we do not obscure this reversal \(Sec\. 5\)\.Table[2](https://arxiv.org/html/2607.26752#S4.T2)both reinforces and complicates the PhysioNet picture\. It reinforces it in one respect: CalTwin again attains the best \(lowest\) ID MSE, and the CMP\-trained heads are again clearly distinguishable from the untrained0\.50000\.5000floor\. It complicates it in three respects that we state precisely rather than average away\. First, FIM\-only does not improve OOD MSE here it is0\.4%0\.4\\%*worse*than baseline \(0\.16820\.1682vs\.0\.16750\.1675\), whereas on PhysioNet the identical penalty gave a7\.0%7\.0\\%reduction\. Second, CMP\-trained AUROC\-OOD is far*above*chance on eICU \(0\.83900\.8390–0\.84350\.8435\) rather than at or below it as on PhysioNet \(0\.47540\.4754–0\.49840\.4984\) a large effect in the opposite direction\. Third, AUROC\-ID for the trained heads is*below*chance on eICU \(0\.26350\.2635,0\.34460\.3446\), the reverse of PhysioNet’s above\-chance ID discrimination\. Consequently CMP\-only, not CalTwin, attains the best value on four of the six columns \(MSE\-OOD, ECE\-ID, ECE\-OOD, AUROC\-OOD\); CalTwin’s only outright win is MSE\-ID\. We return to what this reversal does and does not license us to conclude in Sec\. 5\.

## 5Discussion

Table[1](https://arxiv.org/html/2607.26752#S4.T1)supports three observations that qualify Sections 1–3’s claims on PhysioNet, stated explicitly rather than minimised\.

FIM drives the MSE gain; CMP’s calibration gain is real but small, and the two penalties interact\.FIM\-only reduces OOD MSE by 7\.0% over baseline, CalTwin extends this to 9\.1%, confirming the anchoring benefit of Eq\.[4](https://arxiv.org/html/2607.26752#S3.E4)\. But CMP’s OOD ECE improvement is*smaller*under CalTwin \(0\.7%\) than CMP\-only \(1\.3%\) the combined objective calibrates worse than CMP alone here\. A plausible mechanism: the FIM penalty constrains the shared encoder’s representation along directions useful for next\-state accuracy but not auxiliary\-head calibration, limiting CMP’s ability to redistribute probability mass\. Whether this is an artefact of fixed, untunedλ1,λ2\\lambda\_\{1\},\\lambda\_\{2\}or a structural property of the combined objective is open without a hyperparameter search\.

CMP induces real but non\-transferring discrimination in the auxiliary head \(on PhysioNet\)\.Since the head trains only via CMP \(Sec\. 4\.2\), Baseline/FIM\-only’s exact0\.50000\.5000AUROC reflects an untrained head, not a failure to learn\. CMP\-only and CalTwin reach AUROC0\.57310\.5731/0\.57400\.5740in\-distribution modest but real, given a single linear readout trained 15 epochs/fragment on∼9%\\sim\\\!9\\%\-prevalence data but this collapses OOD to0\.49840\.4984/0\.47540\.4754\(at or below chance\)\. CalTwin’s OOD AUROC is*lower*than CMP\-only’s, mirroring the ECE interaction above\. What Table[1](https://arxiv.org/html/2607.26752#S4.T1)’s AUROC\-ID column rules out is the reading that the head never learns anything useful; the open question is specifically about hospital\-level transfer\.

Evaluation is teacher\-forced, not closed\-loop\.Table[1](https://arxiv.org/html/2607.26752#S4.T1)characterises the one\-step predictor under cross\-fragment/\-hospital shift, with the true previous state fed at every step not the compounding autoregressive\-rollout failure mode of Sec\. 1, which requires closed\-loop, self\-conditioned evaluation we leave to future work\.

The eICU\-CRD result \(Table[2](https://arxiv.org/html/2607.26752#S4.T2)\) does not replicate PhysioNet’s ranking, and we treat that as informative rather than as noise to explain away\.Three differences are large enough that a single\-seed fluctuation is an unsatisfying account of all of them simultaneously\. FIM\-only helps OOD MSE on PhysioNet \(\+7\.0%\+7\.0\\%\) but not on eICU \(−0\.4%\-0\.4\\%, i\.e\. a slight loss\), suggesting the FIM penalty’s benefit is not dataset\-invariant plausibly because eICU’s fragmentation is by genuine hospital identity \(heterogeneous casemix, bed capacity, region\) rather than PhysioNet’s within\-system enrolment\-order proxy, so the two experiments may be probing different magnitudes, or even different kinds, of covariate shift\. CMP\-trained AUROC\-OOD is far above chance on eICU \(≈0\.84\\approx\\\!0\.84\) versus at\-or\-below chance on PhysioNet \(≈0\.48\\approx\\\!0\.48–0\.500\.50\); a plausible explanation is that 24\-hour in\-hospital mortality is an easier signal to extract from ICU vitals than 24\-hour sepsis onset, but we have not tested this and state it as a hypothesis, not a finding\. AUROC\-ID for the trained heads is below chance on eICU but above chance on PhysioNet, which is harder to explain post hoc and is, at face value, more a symptom of instability \(a linear head trained on markedly fewer patients per fragment than PhysioNet provides\) than of either dataset’s calibration properties\. We draw one methodological conclusion from this, not a scientific one: single\-dataset, single\-seed evidence for a shift\-robustness method is not just incomplete but can be actively misleading about which component \(FIM or CMP\) is doing the work, and we would not have known this without running the second dataset\.

Two further open questions remain\. The empirical Fisher approximation \(Eq\.[2](https://arxiv.org/html/2607.26752#S3.E2)\) is known to diverge from the true Fisher under misspecification\[[4](https://arxiv.org/html/2607.26752#bib.bib8)\]; whether this gap matters more for a multi\-step generative predictor than a single\-step classifier is not answerable from our results alone\. And applying CMP to an auxiliary discrete head, rather than the transition distribution directly, is a practical compromise whose principled continuous\-output alternative remains to be derived and tested\.

## 6Conclusion

We have derivedCalTwin, which applies Fisher\-Information shift regularisation and a Confidence Misalignment Penalty jointly to a medical world model’s latent transition predictor, and reported single\-seed feasibility studies on two real multi\-hospital ICU datasets: PhysioNet 2019 \(a documented instance of cross\-hospital covariate shift\[[14](https://arxiv.org/html/2607.26752#bib.bib9)\]\) and the eICU\-CRD Demo, fragmented by genuine hospital identity\. On PhysioNet, FIM reduces OOD next\-step MSE by 7\.0% over baseline and full CalTwin by 9\.1%; CMP’s calibration gain is small \(0\.7% OOD ECE for CalTwin, 1\.3% for CMP alone\), and the CMP\-trained auxiliary head shows modest in\-distribution discrimination \(AUROC≈0\.57\\text\{AUROC\}\\approx 0\.57\) that does not survive the OOD hospital \(≈0\.48\\approx 0\.48–0\.500\.50\) a transfer failure, not an absence of learned signal\. On eICU\-CRD, the ranking does not replicate: FIM\-only does not improve OOD MSE, CMP\-trained AUROC\-OOD is far above chance \(≈0\.84\\approx\\\!0\.84\) rather than at or below it, and CMP\-only rather than CalTwin wins on four of six metrics\. We report both results rather than the more favourable one, because the disagreement between them is itself the most important finding of this feasibility study: it indicates that FIM’s and CMP’s benefits, as instantiated here, are not yet dataset\-invariant, and that a method\-contribution claim resting on either dataset alone would have been unreliable\. Both experiments characterise the one\-step predictor under teacher\-forced evaluation, not the compounding autoregressive\-rollout failure mode motivating the method, and each rests on a single seed\.

Closing the gap to a clinically useful medical digital twin requires, at minimum: running both datasets across multiple seeds to determine whether the FIM/CMP reversal in Sec\. 5 is systematic or an artefact of eICU’s smaller per\-fragment sample size; tuningλ1,λ2\\lambda\_\{1\},\\lambda\_\{2\}on held\-out data rather than using fixed values; evaluating under closed\-loop self\-conditioned rollout; and moving from tabular ICU vitals to the imaging modalities cardiac, fetal ultrasound, surgical video central to this workshop\. We offer CalTwin, both experiments, and this characterisation of its transfer steps as a foundation for that work, and invite collaboration with participants holding access to multi\-site imaging data\.

## References

- \[1\]J\. Chen, Y\. Shi, C\. Yi, H\. Du, J\. Kang, and D\. Niyato\(2024\)Generative\-ai\-driven human digital twin in iot healthcare: a comprehensive survey\.IEEE Internet of Things Journal11\(21\),pp\. 34749–34773\.Cited by:[§2](https://arxiv.org/html/2607.26752#S2.p1.1)\.
- \[2\]C\. Guo, G\. Pleiss, Y\. Sun, and K\. Q\. Weinberger\(2017\)On calibration of modern neural networks\.InInternational conference on machine learning,pp\. 1321–1330\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p5.1),[§3\.3](https://arxiv.org/html/2607.26752#S3.SS3.p1.1)\.
- \[3\]B\. Khan, B\. Mirza, and T\. Syed\(2025\)Causal covariate shift correction using fisher information penalty\.arXiv preprint arXiv:2502\.15756\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p4.1),[§1](https://arxiv.org/html/2607.26752#S1.p6.1),[§2](https://arxiv.org/html/2607.26752#S2.p2.2),[§3\.2](https://arxiv.org/html/2607.26752#S3.SS2.p1.3),[§3\.2](https://arxiv.org/html/2607.26752#S3.SS2.p1.9)\.
- \[4\]B\. Khan, R\. Qureshi, N\. M\. Durrani, and T\. Q\. Syed\(2025\)Confidence\-calibrated covariate shift correction for few\-shot classification in vision\-language models\.InProceedings of the Computer Vision and Pattern Recognition Conference,pp\. 6511–6523\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p6.1),[§2](https://arxiv.org/html/2607.26752#S2.p3.1),[§3\.3](https://arxiv.org/html/2607.26752#S3.SS3.p2.1),[§3\.3](https://arxiv.org/html/2607.26752#S3.SS3.p3.8),[§3\.4](https://arxiv.org/html/2607.26752#S3.SS4.p1.4),[§5](https://arxiv.org/html/2607.26752#S5.p6.1)\.
- \[5\]B\. Khan, T\. Q\. Syed, B\. Mirza, and N\. M\. Durrani\(2025\)Mitigating covariate shift in non\-colocated data with learned parameter priors\.Neurocomputing,pp\. 131656\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p4.1),[§1](https://arxiv.org/html/2607.26752#S1.p6.1),[§2](https://arxiv.org/html/2607.26752#S2.p2.2),[§3\.2](https://arxiv.org/html/2607.26752#S3.SS2.p1.10),[§3\.2](https://arxiv.org/html/2607.26752#S3.SS2.p1.3),[§3\.2](https://arxiv.org/html/2607.26752#S3.SS2.p1.9),[§3\.2](https://arxiv.org/html/2607.26752#S3.SS2.p2.5),[§3\.4](https://arxiv.org/html/2607.26752#S3.SS4.p1.4),[§4\.1](https://arxiv.org/html/2607.26752#S4.SS1.p1.1)\.
- \[6\]J\. Kirkpatrick, R\. Pascanu, N\. Rabinowitz, J\. Veness, G\. Desjardins, A\. A\. Rusu, K\. Milan, J\. Quan, T\. Ramalho, A\. Grabska\-Barwinska,et al\.\(2017\)Overcoming catastrophic forgetting in neural networks\.Proceedings of the national academy of sciences114\(13\),pp\. 3521–3526\.Cited by:[§3\.2](https://arxiv.org/html/2607.26752#S3.SS2.p1.10),[§3\.2](https://arxiv.org/html/2607.26752#S3.SS2.p2.5)\.
- \[7\]T\. J\. Pollard, A\. E\. Johnson, J\. D\. Raffa, L\. A\. Celi, R\. G\. Mark, and O\. Badawi\(2018\)The eicu collaborative research database, a freely available multi\-center database for critical care research\.Scientific data5\(1\),pp\. 180178\.Cited by:[§4\.4](https://arxiv.org/html/2607.26752#S4.SS4.p2.3)\.
- \[8\]M\. A\. Qazi, M\. Nadeem, and M\. Yaqub\(2025\)Beyond generative ai: world models for clinical prediction, counterfactuals, and planning\.arXiv preprint arXiv:2511\.16333\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p1.1),[§2](https://arxiv.org/html/2607.26752#S2.p1.1),[§3\.1](https://arxiv.org/html/2607.26752#S3.SS1.p1.9),[§3\.3](https://arxiv.org/html/2607.26752#S3.SS3.p3.8)\.
- \[9\]M\. A\. Reyna, C\. Josef, S\. Seyedi, R\. Jeter, S\. P\. Shashikumar, M\. B\. Westover, A\. Sharma, S\. Nemati, and G\. D\. Clifford\(2019\)Early prediction of sepsis from clinical data: the physionet/computing in cardiology challenge 2019\.In2019 Computing in Cardiology \(CinC\),pp\. Page–1\.Cited by:[§2](https://arxiv.org/html/2607.26752#S2.p4.1),[§4\.1](https://arxiv.org/html/2607.26752#S4.SS1.p1.1)\.
- \[10\]H\. K\. Rudsari, B\. Tseng, H\. Zhu, L\. Song, C\. Gu, A\. Roy, E\. Irajizad, J\. Butner, J\. Long, and K\. Do\(2025\)Digital twins in healthcare: a comprehensive review and future directions\.Frontiers in Digital Health7,pp\. 1633539\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p1.1),[§2](https://arxiv.org/html/2607.26752#S2.p1.1)\.
- \[11\]C\. Sadée, S\. Testa, T\. Barba, K\. Hartmann, M\. Schuessler, A\. Thieme, G\. M\. Church, I\. Okoye, T\. Hernandez\-Boussard, L\. Hood,et al\.\(2025\)Medical digital twins: enabling precision medicine and medical artificial intelligence\.The Lancet Digital Health7\(7\)\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p1.1),[§2](https://arxiv.org/html/2607.26752#S2.p1.1)\.
- \[12\]H\. Shimodaira\(2000\)Improving predictive inference under covariate shift by weighting the log\-likelihood function\.Journal of statistical planning and inference90\(2\),pp\. 227–244\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p4.1)\.
- \[13\]J\. Snoek, Y\. Ovadia, E\. Fertig, B\. Lakshminarayanan, S\. Nowozin, D\. Sculley, J\. V\. Dillon, J\. Ren, and Z\. Nado\(2019\)Can you trust your model’s uncertainty? evaluating predictive uncertainty under dataset shift\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p5.1),[§3\.3](https://arxiv.org/html/2607.26752#S3.SS3.p1.1)\.
- \[14\]H\. Zhu, J\. Bai, N\. Li, X\. Li, D\. Liu, D\. L\. Buckeridge, and Y\. Li\(2025\)FedWeight: mitigating covariate shift of federated learning on electronic health records data through patients re\-weighting\.npj Digital Medicine8\(1\),pp\. 286\.Cited by:[§1](https://arxiv.org/html/2607.26752#S1.p3.1),[§2](https://arxiv.org/html/2607.26752#S2.p4.1),[§4\.1](https://arxiv.org/html/2607.26752#S4.SS1.p1.1),[§4\.4](https://arxiv.org/html/2607.26752#S4.SS4.p2.3),[§6](https://arxiv.org/html/2607.26752#S6.p1.4)\.