NeurIPS 2026 论文列表

Radio maps are essential for wireless decision-making tasks such as access-point placement, coverage planning, and localization, but their fine spatial details are governed by complex propagation effects and are costly to simulate accurately. Machine learning offers a path to high-fidelity radio-map prediction without running expensive high-fidelity simulations for every scene. However, generating high-quality training labels at scale is also difficult: the affordable labels come from finite-ray simulations, which are richer than low-fidelity inputs but carry residual Monte Carlo noise. We address this challenge with Physics-Unrolled Hybrid Neural Operator (PU-HNO), a three-stage cascade that predicts high-fidelity indoor radio maps from low-fidelity ray-tracing outputs and scene priors by progressively capturing reflection, diffraction, and scattering effects, rather than treating radio maps as generic images. We prove that, under conditionally unbiased label noise, the model can learn stable propagation structure and outperform its own training labels. Experiments across diverse floorplans show that PU-HNO outperforms image-to-image baselines, wireless learning models, and monolithic neural operators across both image-quality and wireless deployment metrics.

We present PhysFormer, a physics-grounded diffusion transformer for generating 4D multi-object mesh dynamics directly in world coordinates. Rather than predicting future frames in pixel space or rolling out next-step system states autoregressively, PhysFormer models physical evolution as full-trajectory coordinate diffusion. Given initial per-vertex positions, velocities, and material conditions, it generates future mesh vertex trajectories in a single denoising process, producing physically plausible object-object and object-environment interactions without hard-coded constraints, simulator priors, or learned shape latents. PhysFormer adopts a DiT-style backbone with factorized temporal, spatial, and object-level attention to capture coherent structure across time, vertices, and objects. Trained on over 100k collision-rich simulated trajectories, it models rigid and deformable multi-object dynamics, generalizes to unseen real-world geometries and larger object counts, and substantially outperforms autoregressive baselines in trajectory accuracy, rigidity preservation, and momentum-based physical consistency. Our results position coordinate-space diffusion as a promising step toward view-invariant, geometry-level world models for robotics, graphics, and physical design.

Understanding how (multimodal) large language models perform on physics problems requires benchmarks that reflect the difficulty and breadth of expert-level physical reasoning. Existing physics benchmarks remain limited in the following two important ways: (1) short of high-difficulty datasets, and (2) lack of comprehensive coverage of visual forms, knowledge points, and step-by-step solution processes. As a result, model performance on current datasets may not be fully representative of their ability to solve complex physics problems. To address these issues, we present \textsc{PhysElite}, a large-scale bilingual multimodal benchmark for Olympiad-level physics reasoning. \textsc{PhysElite} contains 11,586 Olympiad-tier problems. For each problem, we provide corresponding visual diagrams, step-by-step bilingual Chinese--English solution derivations, and the final answer. We benchmark 18 open-source and closed-source MLLMs, and find that even the strongest model reaches only 33.7\% answer accuracy. We additionally conduct step-level process evaluation to diagnose where models fail in the reasoning chain. The benchmark results and dataset will be publicly available.

Physics-based digital twins aim to predict the dynamics of real-world objects under interaction, enabling real-to-sim-to-real applications in robotics. Current approaches reconstruct such twins as explicit physical models (such as spring-mass systems) to predict the dynamics, but the resulting models often inherit the resolution of the visual reconstruction rather than being reduced to the physical complexity required to reproduce task-relevant dynamics. This mismatch introduces redundant topology, making repeated forward-dynamics rollouts unnecessarily expensive. To address this challenge, we present PhySPRING, an fully differentiable GNN-based method to reduce complexity in spring--mass digital twins. PhySPRING jointly learns a hierarchy of coarsened graph topologies and their mechanical parameters from observations. At each reduction level, PhySPRING merges nodes with similar learned dynamic responses to optimize the topology, while maintaining every reduced layer as an explicit spring--mass system. On the PhysTwin benchmark, PhySPRING improves dense reconstruction and prediction accuracy over PhysTwin, while reduced models retain stable physical and visual fidelity with up to a 2.30$\times$ speed-up. We further demonstrate the effectiveness of PhySPRING in a Real2Sim robot policy-evaluation pipeline, where the reduced models are substituted zero-shot into ACT and $\pi_0$ evaluations, maintaining comparable manipulation success rates across downsampling levels while improving action-sampling effectiveness. Together, PhySPRING enables efficient and structure-preserving spring--mass reduction without sacrificing fidelity or robotic utility.

Physics-informed neural networks (PINNs) train a single neural approximation by minimizing multiple physics- and data-derived losses, but the gradients of these losses often interfere and can stall optimization. Existing remedies typically treat this pathology either through scalar loss balancing or full-parameter-space gradient surgery, leaving it unclear which intervention is most appropriate. We show that PINN gradient conflict is not a uniform failure mode with one universal remedy. Instead, we identify distinct PINN gradient-conflict regimes, each associated with a different intervention class. Persistent directional conflict may require separate loss-indexed parameter subspaces, magnitude imbalance often favors scalar reweighting, and low or transient conflict may require no extra mitigation. To select between scalar reweighting and a lightweight architectural intervention, we propose a diagnostic-first framework. It profiles a 1000-step unmodified PINN run and, when intervention is warranted, uses one low-rank adapter per loss to create explicit loss-indexed parameter subspaces attached to a shared PINN trunk, providing each loss with a direct gradient pathway. Across more than 60 PDE configurations, including forward, inverse, multi-physics, parameter-varying, and high-dimensional problems up to 50D, persistent directional conflict dominates standard forward $K=3$ benchmarks and a natural $K=4$ thermoelastic system, where adapters combined with reweighting yield significant improvements. In contrast, $K=3$ inverse problems and natural $K=5$ and $K=6$ multi-physics systems are largely magnitude-dominated and often favor reweighting alone, while full-parameter-space gradient surgery can fail on heterogeneous parameter spaces. A regime-transition theorem and a blockwise neural tangent kernel analysis explain why gains from these separate adapter parameter subspaces arise selectively in persistent-conflict regimes.

Multi-modal cloud removal exploits complementary optical and synthetic aperture radar (SAR) images to restore cloud-degraded remote sensing images. Most existing methods rely on black-box, data-driven architectures with limited interpretability of cross-modal interactions. Although some attempts introduce physical priors into networks, their oversimplified formulations fail to faithfully characterize the underlying physical imaging process and the networks remain loosely coupled with optimization variables. To address these issues, we propose a physics-informed deep unfolding network for cloud removal via optical-SAR image fusion, termed as PIU-CR. We first formulate cloud removal as a physics-informed optimization problem. Specifically, we fundamentally ground the optimization in the physical imaging mechanism of cloud degradation by embedding the atmospheric scattering model into data fidelity term. Then, the regularization terms establish an explicit cross-modal interaction mechanism, overcoming the single-modal information scarcity and the obscure, uninterpretable interactions in black-box models. They are dedicated to SAR-guided structure and spectral regularization, jointly introducing cross-modal structural feature alignment and coordinated spectral consistency constraints. The resulting optimization problem is then unfolded into a multi-stage neural network with dedicated structure and spectral branches. Each stage corresponds to explict optimization iteration step, enabling interpretable and effective reconstruction process. Experiments demonstrate that the proposed method outperforms state-of-the-art methods.

The Physics-Informed Neural Network (PINN) literature has produced a rapidly expanding catalogue of methods. We divide a PINN training pipeline systematically into four components and observe that many existing benchmarks study these components in isolation. These components are domain-importance adaptation, loss balancing, the neural network architecture, and the optimization scheme. Moreover, the studies set the surrounding and not considered components of the pipeline to a minimal default that is no longer representative of current best practice approaches. Conclusions drawn under such conditions lead to suboptimal results. In this work, we propose a new evaluation protocol that (1) treats the four components as an integrated system; (2) requires as a key aspect a competitive implementation of the components not currently under investigation; (3) specifies the metrics and reporting format, and (4) is accompanied by structured documentation that ensures the traceability of evaluations across studies. Based on this comprehensive protocol, we release with PINNeval an innovative JAX package containing 18 different methods from the current literature as well as nine efficiently implemented benchmark problems. Using PINNeval, we illustrate our evaluation protocol in relation to established benchmark studies and report on results that challenge established assumptions.

Full-space electron density generation is fundamental to modeling molecular quantum states, ground-state properties, and chemical interactions. DFT provides a principled route to electron density, but high-fidelity calculations require costly self-consistent iterations, limiting large-scale quantum-chemical modeling. Deep learning offers a promising surrogate, yet existing methods often rely on indirect density-related prior, including coordinate queries, predefined basis functions, orbital coefficients, or spherical atomic density grids. These prior introduce reconstruction overhead and can hinder continuous full-space modeling across sharp nuclear cores and sparse vacuum regions. Here, we introduce PI-EDG, a physics-informed voxel-space framework that maps molecular geometries directly to full-space electron-density fields by combining quantum-mechanical prior injection, hybrid FNO-CNN modeling of local and non-local interactions and magnitude-aware DS-LMoE routing for extreme density ranges. On EDBench, PI-EDG achieves an MAE of 3.405$\times$10$^{-3}$, a total electron-number MAE of 0.472, and an average inference time of 133.4 ms for one molecule. Compared with graph-based, basis-based, and voxel-based baselines, PI-EDG demonstrates better predictive accuracy, improved robustness across extreme density regimes, and better physical consistency while maintaining efficient full-space generation. These results suggest that PI-EDG offers a new, direct, and efficient route for accelerating DFT-based electron density calculations.

Motivated by the success of large language models (LLMs) with broad generalizability and robustness to noisy or unreliable pre-training data, we seek to bring similar capabilities to PDE solvers. In addition, inspired by the posterior predictive mean-based inference mechanism of the in-context learning in prior-data fitted networks (PFNs), we propose PDE-PFN, a prior-data fitted neural solver that approximates the posterior predictive mean of PDE solutions via in-context learning. PDE-PFN builds on a PFN architecture with self- and cross-attention mechanisms of Transformer and is pre-trained on noisy approximate solutions generated by physics-informed neural networks, serving as diverse but not necessarily exact priors. Through experiments on a range of two-dimensional PDEs, we demonstrate that PDE-PFN achieves empirical generalization across heterogeneous equations, robustness under noisy priors, and zero-gradient-update in-context inference capability. Our approach not only outperforms task-specific baselines but also provides a flexible and robust framework for advancing SciML.

Scientific machine learning has opened new avenues for solving parameterized partial differential equations (PDEs), enabling models to learn a family of PDEs and generalize to unseen instances. In this context, data-driven operator learning methods typically require large training datasets, while physics-informed neural networks (PINNs) suffer from difficult optimization and limited generalization, especially for nonlinear PDEs. We propose Newton-PINet, a physics-informed network enhanced by Newton linearization, offering an effective meta-learning framework for nonlinear PDEs. Newton-PINet (i) employs a physics-informed multilayer network with skip connections, where the output-layer weights are solved by least squares; (ii) adopts a two-stage learning strategy that first leverages gradient-based training to learn robust representations from the available training tasks, and then performs gradient-free fine-tuning on the output layer for fast task-specific generalization; and (iii) incorporates a Newton linearization method to speed up the least-squares iteration for nonlinear PDE problems. On a challenging nonlinear reaction-diffusion benchmark, Newton-PINet achieves up to three orders of magnitude lower relative error than recent neural solvers, while using 16× fewer training tasks and over an order of magnitude less training time (under 5 minutes versus several hours). This work advances the meta-learning of PINNs toward data-efficient, fast, and generalizable physics solvers. The datasets and code are provided in the supplementary material.

Local field potentials (LFPs) are population-level neural signals central to brain-computer interfaces and systems neuroscience, yet unlike spike-based population codes, their dynamics lack a principled geometric description that connects spectral structure to latent state-space geometry. Here we establish, analytically and empirically, that the lag-embedded dynamics of LFP signals lie on a low-dimensional K-torus, where K equals the number of sustained oscillatory modes present in the signal. Modeling LFPs as bounded autoregressive processes, we show that each oscillatory component contributes an independent circular degree of freedom, while aperiodic 1/f structure and noise contribute only geometric thickness around the manifold without altering its topology. To apply this theory to real nonstationary recordings, we introduce DeepLagField, a physics-informed network that jointly estimates time-varying AR structure and effective model order, with formal guarantees that local toroidal geometry is preserved despite drifting oscillatory dynamics.We validate the predicted toroidal geometry using persistent homology across primate visual cortex LFP, rodent hippocampal LFP, and mouse cortical EEG recordings, confirming the expected Betti number signatures across species and recording modalities. Critically, we demonstrate that this geometric structure is not merely descriptive but carries behaviorally relevant information inaccessible to standard spectral summaries — as evidenced by torus parameters derived purely from manifold geometry outperforming multi-band spectral features for sleep-state decoding without any hand-crafted frequency design. This proof of concept points toward broad downstream utility wherever oscillatory field signals are recorded, from neural decoding and brain-state monitoring to clinical biomarker development. These results reframe neural oscillations not as isolated spectral features but as coordinate directions of a low-dimensional delay manifold, opening a geometry-first approach to neural signal analysis that is simultaneously theoretically grounded, empirically validated across species, and predictive of behaviorally relevant brain states.

In this paper, we tackle the critical failure modes of Physics-Informed Neural Networks (PINNs), such as spectral bias, which lead to poor convergence on complex PDEs. We identify two key shortcomings in existing curriculum learning methods for PINNs: unreliable knowledge transfer between stages and a reliance on manual, ad-hoc curriculum design. To overcome these limitations, we present Neural Operator-based Curriculum Learning (NOCL), a unified framework that leverages Neural Tangent Kernel (NTK) theory to automate curriculum generation and employs neural operators to enable robust, dynamic knowledge transfer across curriculum stages. By dynamically training neural operators and filtering data for PINN initialization, our approach ensures scalable and effective learning across progressively difficult tasks. Experiments verify that NOCL leads to marked gains in convergence and generalization relative to prior methods, resulting in substantially better performance on test suite.

Many engineering building blocks behave as multi-port linear time-invariant systems. RF cavities, photonic devices, and superconducting quantum chips, despite their different underlying physics, all share a common mathematical structure for their port-level response. Each entry of the response matrix is a sum of contributions from a small number of intrinsic resonant modes, the pole-residue form. A model capable of predicting such responses for arbitrary geometries and arbitrary port configurations, while simultaneously extracting the underlying eigenmode structure, would therefore establish a foundational design principle spanning all these domains. We propose a neural framework that learns this modal decomposition end-to-end, supervised only by system-level observables and without supervising the modal parameters themselves. The architecture decomposes into a port-independent pole predictor and two port-dependent coupling predictors whose outputs are combined entry-wise, separating intrinsic from port-dependent features. This factorization yields a single trained model that generalizes to port counts unseen during training, dissolving the $\mathcal{O}(N^2)$ scaling barrier of direct regression. Despite no modal supervision, the freely-parameterized poles converge to physically meaningful eigenmodes, verified by cross-validation against the AAA rational approximation algorithm. We instantiate the framework in radio-frequency electromagnetic surrogate modeling. A model trained only on 2-port data accurately predicts $N$-port responses unseen during training.

Inverse problems for stiff parabolic partial differential equations (PDEs), such as the inverse heat conduction problem (IHCP), are severely ill-posed: the forward map rapidly damps high-frequency interior structure before it reaches the boundary. Soft-constrained physics-informed neural networks (PINNs), which embed the PDE as a residual penalty, suffer from gradient pathology in this regime and tend to fit boundary measurements while leaving the interior field essentially untouched. We propose Neural Field Thermal Tomography (NeFTY), a hard-constrained neural field framework for label-free three-dimensional inverse heat conduction. NeFTY represents the unknown diffusivity as a continuous coordinate-based neural network, and at every optimization step passes the candidate field through a differentiable implicit-Euler heat solver with harmonic-mean interface flux, so that the governing PDE holds exactly on the discretization rather than as a soft penalty. Adjoint gradients propagate the surface reconstruction error back to the network weights at solver-level memory cost, making test-time inversion tractable on a single GPU. Across synthetic 3D benchmarks, NeFTY substantially outperforms soft-constrained PINN variants and a voxel-grid baseline on label-free volumetric recovery, and it transfers to real thermography data, surpassing classical signal-processing baselines in both defect segmentation and depth estimation.

Differentiable physics solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented. Integration effort, computational cost, gradient accuracy, and numerical conditioning vary widely across solvers and are discoverable only by trial and error. We introduce Mosaic, an extensible benchmarking framework for differentiable PDE solvers that standardizes access to solver gradients. Each solver is packaged as a containerized component (Tesseract) exposing a uniform gradient API regardless of language or automatic differentiation (AD) strategy, enabling researchers to evaluate, compare, and build on non-trivial physical solvers. Our evaluation of 14 solvers across fluid dynamics, structural mechanics, and heat transfer demonstrates that the benchmark surfaces practically relevant differences: order-of-magnitude variation in computational cost and Jacobian conditioning, alongside structural incompatibilities that eliminate solvers from realistic tasks entirely. Despite this variation, all solvers that produce gradients converge to similar optima, indicating that the practical barriers are memory limits, numerical stability, and setup compatibility rather than gradient accuracy alone. Mosaic is open-source and available at https://anonymous.4open.science/r/mosaic-bench.

Whether navigating a building, operating a robot, or playing a game, an agent that acts effectively in an environment must first learn an internal model of how that environment works. Partially observable Markov decision processes (POMDPs) provide a flexible modeling class for such internal world models, but learning them from observation-action trajectories alone is challenging and typically requires extensive environment interaction. We ask whether language-model priors can reduce costly interaction by leveraging prior knowledge, and introduce Pinductor (POMDP-inductor): an LLM proposes candidate POMDP models from a few observation-action trajectories and iteratively refines them to optimize a belief-based likelihood score. Despite using strictly less information, Pinductor matches the performance and sample efficiency of LLM-based POMDP learning methods that assume privileged access to the hidden state, while significantly surpassing the sample efficiency of tabular POMDP baselines. Further results show that performance scales with LLM capability and degrades gracefully as semantic information about the environment is withheld. Together, these results position language-model priors as a practical tool for sample-efficient world-model learning under partial observability, and a step toward generalist agents in real-world environments.

Protein Language Models (PLMs) have made remarkable progress following scaling laws established in natural language processing across sequence- and structure-based tasks, yet the potential of tokenization remains underexploited. Unlike human language, proteins preserve structure despite extensive sequence variation — a property standard tokenization strategies fundamentally fail to capture. We introduce ZEST (Zoned Encoding of Sequence Traits), an evolution-informed vocabulary derived from conserved regions of multiple sequence alignments. ZEST allows embedding domain-level biological priors directly at the tokenization stage rather than learning them implicitly through scale. ZEST natively compresses sequences to an average token length of 4 residues, enabling our model to process 4,000 residues within a standard 1024-token context window. Building on this, we present LEMON (Layered Extraction of Molecular Ordering from Nature), a compact 200M-parameter sequence-based model for detection of remote homology between protein sequences trained on a single H100 GPU for one week. Despite its modest size, LEMON outperforms state-of-the-art models ranging from 600M to 3B parameters. Our results demonstrate that evolution-informed tokenization can substitute for massive parameter scaling, opening a new direction for efficient, biologically-grounded protein representation learning. All code, model weights, and results are publicly available under the MIT license.

Operator learning has experienced a shift toward attention-based architectures. This trend has more recently extended to physics-informed operator learning, where stacked cross-attention blocks add considerable computational cost relative to the foundational PI-DeepONet. We ask whether this complexity is necessary. Starting from the DeepONet branch-trunk decomposition, we replace the bilinear readout with a single softmax-weighted readout in which the trunk emits a query vector and the branch emits a set of key-value pairs—a structure we show admits universal approximation via reduction to a simplex-bilinear form. The resulting architecture, KerONet, uses no iterated attention, layer normalization, or explicit learnable projection matrices. Under a unified hyperparameter optimization protocol with a strict $200{,}000$-parameter budget, we evaluate KerONet alongside iterated-attention architectures (PIT, PINTO) and PI-DeepONet on four canonical 1D PDEs whose solutions range from globally smooth to sharply localized. KerONet outperforms PIT and PINTO on every PDE, across all five seeds, in accuracy (approximately $2$–$4\times$ lower rel-$L^2$ error), reproducibility ($2$–$31\times$ lower standard deviation), and speed ($1.8$–$4.4\times$ faster training time). Against PI-DeepONet, KerONet shows substantial gains where input-dependent localized features dominate ($2.5$–$8\times$ lower error on Burgers and Allen-Cahn) while exhibiting comparable accuracy on smoother operators (advection and diffusion-reaction)–a balance the iterated-attention architectures do not achieve. Our findings demonstrate that iterated cross-attention is not necessary to realize the benefits of query-dependent feature mixing in physics-informed operator learning.

We study the problem of efficient online reinforcement learning in the infinite horizon setting when there is an offline dataset to start with. We assume that the offline dataset is generated by an expert but with unknown level of competence, i.e., it is not perfect and not necessarily using the optimal policy. We show that if the learning agent models the behavioral policy (parameterized by a competence parameter) used by the expert, it can do substantially better in terms of minimizing cumulative regret, than if it doesn't do that. We establish an upper bound on regret of the exact informed PSRL (iPSRL) algorithm that scales as $\tilde{\mathcal{O}}(\sqrt{T})$. This requires a novel prior-dependent regret analysis of Bayesian online learning algorithms for the infinite horizon setting. We then propose the informed RLSVI (iRLSVI) algorithm to efficiently approximate the iPSRL algorithm. Empirical results show that small offline expert datasets are sufficient for iRLSVI to outperform online-only algorithms on hard exploration domains.