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该论文提出 Normalizing Flow Maps（NFM），一种可精确求逆的推前映射类模型，统一了 normalizing flows 与 flow maps，支持高效的精确似然评估与少步生成。在 CIFAR-10、ImageNet-64 条件图像生成和 Boltzmann Generators 平衡采样任务上达到了参数量匹配条件下 normalizing flows 的最先进水平。
该论文提出CGDT-CESN——一种基于变量相关性引导并进行跨簇权重训练的聚类回声状态网络，用于多变量时间序列预测，在Twitter信息级联与太阳风预测数据集上优于传统ESN。
This paper shows that null controls alone are insufficient for validating scientific discovery and interpretability systems, demonstrating that acceptance tests like closure can be passed by scientifically empty candidates, and proposes combining multiple criteria to both accept genuine results and reject nulls.
清华团队提出 Controlled-Minimax 框架，将对抗训练动力学建模为二阶 ODE，并通过设计反馈控制器为 minimax 优化提供局部指数稳定性保证，有效抑制 GAN 训练中的振荡与极限环问题。
该论文研究了在稀疏噪声传感器观测下，神经代理模型在空间窗口与历史时间之间的输入分配权衡，并通过贝叶斯最优误差分析与 Burgers、Kuramoto-Sivashinsky 方程实验，给出了窗口按场的相关长度设定、输入预算随预测时距调整的设计规则。
This arXiv paper reports 'constraint-induced self-organization via geometric radiation,' a mechanism for dynamic order in closed, far-from-equilibrium systems, demonstrated across three geometric flows in a coupled Ricci flow system. It introduces a novel 'wedge-shaped attractor' topology and proves four theorems establishing sufficient conditions for a universal stress-accumulation-to-fractal-limit-cycle process.
A NeurIPS 2026 paper introducing DynaBase, a minimal interpretable architecture for zero-shot reconstruction of dynamical systems built from just a one-parameter piecewise affine map and a context selector. Despite its simplicity, it outperforms major time-series and dynamical-systems foundation models on long-term statistics and short-term predictions, and offers a tractable mathematical basis for analyzing such models.
A NeurIPS 2026 paper introduces topological out-of-domain generalization for dynamical systems reconstruction, identifying failure modes in hierarchical DSR models and fixing them with feature-splitting and physical sparsity priors, enabling correct prediction of bifurcations and regime changes without explicit control-parameter knowledge.
The paper introduces Continually-Recyclable Unit-Gating (CRUG), a parameter-isolation continual learning method for dynamical systems reconstruction that uses L0-regularized differentiable gates to allocate and recycle units across tasks, achieving zero forgetting and a strong reconstruction-capacity trade-off on nonlinear and chaotic systems.
The paper proposes EnJoi, an ensemble joint score filter for generative data assimilation that learns the joint distribution of past and future states, enabling a modified En4DVar approach to balance confidence in the current state versus new observations. Experiments on fluid and traffic flow simulations show improved reconstruction, especially with sparse, non-homogeneous observations.
The paper shows that small autoregressive transformers trained only on restricted parameter regimes of nonlinear dynamical systems (logistic/sine maps, Lorenz, Hopf) can extrapolate global dynamics far outside the training distribution, reproducing period-doubling cascades up to period 128 and the Feigenbaum constant to within 5e-4, with causal interventions revealing how control-parameter information flows through attention.
The article explores mathematical billiards, including varieties like inner billiards, and discusses using computer experiments to study trajectories in dynamical systems.
This paper investigates whether the recurrence in selective state space models drives tokens to consensus similar to attention in transformers, using dynamical systems theory to analyze stability and attraction domains for time-varying weight matrices.
This paper presents K2SVD, a principled method for learning Koopman operator representations with Kalman inference to achieve efficient and accurate time-series prediction, demonstrating superior performance over existing state-of-the-art approaches.
The paper introduces Fundamental Dynamical Units (FDUs) as composable primitives for physics-informed structural inference in networked dynamical systems, using neural ODEs to recover interaction structures from perturbation time-series data.
This paper presents a method to autonomously generate the full 'Bad Apple' video using a small recurrent dynamical system with 417k parameters, trained from a single initial state. It details the architecture, training techniques like rollout horizon curriculum and state perturbation noise, and shares code and models on GitHub.
This paper presents a novel approach to simulating coupled dynamical systems by using neural surrogates and self-consistency to solve fixed-point problems over full trajectories, replacing traditional timestep-by-timestep integration. It demonstrates the method on van der Pol oscillators and Hodgkin–Huxley neuron networks, highlighting efficiency gains and unique gradient properties.
This paper introduces Sparse Koopman Autoencoders (SKAEs) to identify local dynamical regimes in multibasin nonlinear systems, demonstrating superior forecasting performance and interpretable latent supports.
MnemoDyn is a dynamical-systems based model trained on 40K fMRI sequences for learning resting-state dynamics, outperforming transformer-based approaches in reconstruction quality and generalizing well across diverse populations.
This paper presents a black-box method for LLM safety classification using dynamical systems and Koopman operators on prompt-response embedding dynamics to detect unsafe outputs.