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Introduces Weak-form Kernel Ridge Regression (WKRR) for learning dynamical systems from noisy measurements, combining a weak formulation with kernel ridge regression to filter noise and improve accuracy. The method outperforms baseline methods on chaotic benchmarks up to 64 dimensions and 15,000-dimensional real-world fluid data.
Proposes SNAP-FM, a method that leverages sparse GPU nonlinear optimization to accelerate constraint projection in physics-constrained generative modeling, achieving faster inference while preserving exact physical constraint satisfaction.
This paper presents MCO-PDE, a competitive optimization framework that discovers shared partial differential equations from multiple observational datasets by combining neural surrogates, soft-competitive weighting, and genetic algorithms for structure search. It demonstrates high accuracy in recovering canonical equations from limited data and handles complex geometries and real-world experiments.
This paper introduces a model-free deep learning method for solving high-dimensional nonlinear partial differential equations with unknown coefficients, using zeroth-order derivative estimators derived from perturbed Monte Carlo trajectories. The approach avoids automatic differentiation, provides theoretical error bounds, and demonstrates competitive performance in numerical experiments.
Operator Boosting is a stagewise residual-learning framework that constructs compact neural operator surrogates for PDEs by training tiny models on residual fields. It achieves accuracy comparable to or better than full-size models while reducing parameters by up to 95%, demonstrating Pareto improvements on several benchmarks.
This paper presents an advanced GNN surrogate for forecasting CO2 plume migration in complex geological formations, introducing an anisotropic message-passing mechanism to handle directional transport, aiming to accelerate carbon capture and storage simulations.
Physics-conforming Latent Twins is a framework for learning latent surrogate solution operators that enforce physical principles such as conservation laws and dissipative inequalities by design, using a constraint-transfer approach and structure-preserving latent dynamics.
This paper explores the use of variational autoencoders to learn latent representations of large-scale X-ray scattering data, enabling efficient data compression and analysis.
This paper introduces Separable Neural Architecture (SNA), a function class that combines neural approximation with tensor decomposition to efficiently solve parametric PDEs. The method achieves dramatic speedups (up to 150,000×) over traditional grid-based methods in engineering applications like laser powder bed fusion and material property prediction.
This paper proposes structure-preserving neural surrogates for partial differential equations that integrate Gaussian process regression to provide tractable uncertainty quantification, enabling real-time simulation with closed-form error estimates.
SirenFNO leverages sinusoidal representation networks to learn full-frequency Fourier kernels, eliminating frequency truncation and achieving significant parameter reductions while improving accuracy on PDE benchmarks.
This paper studies transfer specificity in implicit neural representations across SIREN, ReLU MLPs, and Fourier-feature MLPs, finding that transfer magnitude and specificity depend on architecture, with ReLU being more selective and SIREN reusing weights broadly. Results suggest architecture selection should consider explicit control conditions, not just transfer magnitude.
Proposes OTP-FM, a novel method for multimarginal flow matching that uses optimal transport potentials to softly steer flows through intermediate marginals, achieving state-of-the-art performance on single-cell RNA sequencing, oceanographic, and meteorological datasets.
The paper describes a metric-aware hybrid forecasting system for the CTF4Science Lorenz challenge, combining neural denoisers, ODE fitting, and histogram-tail substitution to optimize different metrics across nine task pairs, achieving a public leaderboard score of 83.85529.
This paper proposes a history-bootstrapped autoregressive flow matching method for reconstructing full spatiotemporal fields (velocity and temperature) from partial observations of boiling dynamics, addressing the ill-posed inverse problem with non-Markovian posterior.
This paper identifies a consistent three-regime structure in scientific machine learning models, showing that optimization effectiveness is regime-specific and can challenge conventional loss-landscape interpretations. It proposes a regime-aware diagnostic framework validated across PINNs, neural operators, and neural ODEs.
This paper presents a comprehensive mathematical framework for sequential surrogate modeling of three-phase black-oil reservoir dynamics using Fourier Neural Operators (FNO) and physics-informed variants (PINO), applied to the Norne benchmark reservoir. Theoretical contributions include functional-analytic formulation, covariate shift analysis, physics-constrained spectral stability, and truncated backpropagation gradient analysis.
Proposes semigroup consistency as a diagnostic for evaluating learned physics simulators, showing that normalized semigroup error correlates with rollout degradation in heat and Burgers dynamics using ConvNet and FNO baselines.
The paper introduces beignet, a PINN architecture that replaces random Fourier features with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy and computational efficiency on PDE benchmarks.
Introduces Multi-Agent Residual In-Context Learning (MARICL), an agentic framework that uses LLM agents to analyze residuals from a base model on tabular data, hypothesize missing structure, and produce explicit correction terms via textual gradient optimization. Across nine benchmarks, MARICL consistently improves over its base model and demonstrates mechanistic generalization in cell-free protein predictions.