NeurIPS 2026 论文列表

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.

We introduce PINNBench, a benchmark and evaluation study for training-policy selection in hybrid PINN-operator PDE solvers, contributed to the NeurIPS 2026 Evaluations and Datasets (ED) Track. PINNBench comprises 1,539 recorded runs and probes across 13 PDE configurations drawn from 8 equation families, 3–5 training policies per PDE, and 10 seeds per condition, with seven standardized metrics, Wilcoxon signed-rank tests, paired bootstrap 95% confidence intervals, Cohen's d, and Benjamini–Hochberg FDR correction. Baseline evaluation of 5 routing methods establishes three findings that bear directly on how PDE solvers should be evaluated. (i) No single policy dominates: hybrid_full wins 7/13, hybrid_no_gate 4/13, pinn_only 2/13. (ii) Accuracy and regret dissociate: under relative L2, a physics-loss heuristic and a learned Random Forest router reach identical 62% top-1 accuracy, but the heuristic suffers mean regret 0.0850 versus 0.0011 — a 77x gap. Evaluation by accuracy alone is misleading for PDE policy routing. (iii) Causal-loss effectiveness is stage-mediated: 7/9 PDEs improve with pretraining (+5.9% mean) while 5/9 degrade without it (-4.2%). A new leave-one-PDE-family-out evaluation shows that the strongest family-level generalizer uses no PDE-identity features, addressing the concern that PDE-aware routing memorizes PDE identity. All 1,539 result JSONs, PDE implementations, policy configurations, statistical pipeline, and routing infrastructure are released as open-source artifacts.

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.

The success of vision transformers—especially for generative modeling—is limited by the quadratic cost and weak spatial inductive bias of self-attention. We propose PDE-SSM, a spatial state-space block that replaces attention with a learnable convection–diffusion–reaction partial differential equation. This operator encodes a strong spatial prior by modeling information flow via physically grounded dynamics rather than all-to-all token interactions. Solving the PDE in the Fourier domain yields global coupling with near-linear complexity, delivering a principled and scalable alternative to attention. We integrate PDE-SSM into a flow-matching generative model to obtain the PDE-based Diffusion Transformer PDE-SSM-DiT. Empirically, PDE-SSM-DiT matches or exceeds the performance of state-of-the-art Diffusion Transformers while substantially reducing compute. Our results show that, analogous to 1D settings where SSMs supplant attention, multi-dimensional PDE operators provide an efficient, inductive-bias-rich foundation for next-generation vision models.

Photonic crystal fibres (PCFs) underpin critical applications in telecommunications, sensing, and high-power laser delivery, yet their design remains a manual, expert-intensive process that couples geometric intuition with deep waveguide physics. Vision-language models (VLMs) offer a promising path toward automating this pipeline, but can they truly reason about photonic physics from microscopy images, or do they merely recognise visual patterns? We introduce PCFBench, the first comprehensive benchmark for evaluating VLMs on the complete photonic inverse-design workflow. PCFBench spans 26 tasks organised into six categories of increasing cognitive demand (Geometry Perception, Physics Understanding, Text Generation, Multi-modal Reasoning, Inverse Design, and Code Generation), built from over 220K FDTD simulation samples across 18 structurally diverse fibre families. We evaluate both individual VLMs on isolated tasks and multi-agent systems (MAS) on the full sequential pipeline from perception to design. Our results reveal a striking perception-design gap: current models can identify fibre geometry with moderate success, yet consistently fail to translate that visual understanding into physics-aware design actions. Moreover, cascading agents through the pipeline exposes significant error propagation, where upstream perception mistakes compound into downstream design failures. These findings suggest that neither model scaling nor naive agent chaining suffices; closing the loop demands explicit physical grounding. PCFBench provides the community with a rigorous, multi-dimensional testbed to measure progress toward AI-assisted photonic engineering.

We demonstrate that AI agents can autonomously improve mathematical proofs of quantitative results. As a key step towards this frontier, we achieve strict improvements on Grothendieck's and Korenblum's constants, whose precise values have remained surprisingly elusive despite their recurrence in both the mathematical and physical sciences. By encoding relevant literature as a partially formalized Lean blueprint, we structure the agent's search space to localized proof refinements that automatically propagate to a verified final bound. Concretely, Grothendieck's constant ($\mathcal{K}_G$) is shown to be: $$ \mathcal{K}_G \leq \tfrac{\pi}{2 \log (1 + \sqrt{2})} - 10^{-17}, $$ which is the first explicit numerical improvement since Krivine's landmark 1979 result. For Korenblum's constant ($\mathcal{K}_K$), the lower bound is tightened to: $$ \mathcal{K}_K \geq 0.3554 + 0.001165, $$ a third-digit improvement over Wang's recent 2025 result. In summary, we establish that AI agents can autonomously refine formal proofs of open problems and provide a generalizable framework for future mathematical discovery.

Characterizing the features of a Hamiltonian that governs a quantum system serves as a fundamental subroutine of quantum device calibration, signal sensing, and error correction. Recent works proposed protocols have achieved the optimal Heisenberg-limited scaling learning ansatz-free Hamiltonians from their real-time evolutions without fully specifying interaction structures. However, these protocols relies on both deep circuits with interleaving probes and control, and extremely short time resolution, making them difficult to implement on near- and intermediate-term in situ quantum experiments. In this work, we propose a computational efficient, *control-free*, and *ancilla-free* algorithm that uses only *Pauli product state preparation and measurement*, and learns an ansatz-free Hamiltonian $H$ with $||H||\leq\Lambda$ in total evolution time of $\Theta(\tfrac{\Lambda}{\epsilon^2}\log(\tfrac{\Lambda}{\epsilon}))$. The evolution time cost of our algorithm is *optimal* for any control-free protocols as we further prove a lower bound of $\Omega(\tfrac{\Lambda}{\epsilon^2}\log(\tfrac{\Lambda}{\epsilon}))$. Technically, our method introduces a randomized-sampling framework that combines band-limited kernel-based time sampling with a displacement sieve for Hamiltonian structure learning. The characteristic probe time resolution depends only on $\Lambda$ instead of $\varepsilon$, which makes our protocol especially appealing in the high-precision regime for sensing and calibration applications.

Understanding model predictions is essential for physical applications, where outputs often inform safety-critical decisions, such as structural load assessment, weather warnings, and clinical diagnosis. Shapley values satisfy many desirable properties as an attribution method, but their computational cost during inference hinders their practical use. Current amortized explainers, such as FastSHAP, are limited to homogeneous inputs, which is problematic for physical applications where data often comes from irregular grids and geometries. We introduce OperatorSHAP, a grid-agnostic attribution method and training procedure that allows us to train FastSHAP-like explainers for neural operators. We establish a theoretical framework for attributions in function space, connecting to Aumann–Shapley values. We further show that OperatorSHAP's explanations are consistent with state-of-the-art discrete Shapley values across resolutions and transfer across grid sizes without retraining.

Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to capture bias, but suffers from parameter–discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit both gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are not robust to abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, we integrate BRPC with restart mechanisms that detect regime shifts and reset the calibration process, yielding a unified approach to mixed nonstationarity. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical results on synthetic and plant-simulation benchmarks demonstrate that BRPC improves calibration accuracy under gradual changes, while the restart-augmented framework further enhances robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

Neural quantum states (NQS) provides a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov-chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a trust-region algorithm that clips probability-ratio changes in the amplitude channel and wrapped phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across inner updates, and preserves the scalability of first-order optimization. Across Ising, Heisenberg, and frustrated $J_1$--$J_2$ spin chains, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a $1.5$B-parameter RWKV-7 model as a neural quantum state, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.

We study preference-based bandits with general reward function classes, where a learner sequentially selects pairs of arms and observes binary preference feedback governed by the Bradley-Terry model. This setting naturally arises in applications such as recommender systems, tournament ranking, and learning from human feedback, where relative preferences are easier to elicit than absolute rewards. The observation model inherits the logistic bandit challenge of handling the problem-dependent constant $\kappa$, which accounts for the non-linearity of the link function and can grow arbitrarily large. Moreover, prior work has predominantly focused on linear or kernelized reward models, precluding the use of richer function classes. To address these limitations, we consider general reward function classes and introduce the *locally sensitive eluder dimension*, a novel complexity measure tailored to the logistic structure of preference feedback that yields fine-grained regret guarantees without unfavorable dependence on $\kappa$. Building on this notion, we propose **GINOP** (**G**eneric **IN**formative **OP**timism), an algorithm that constructs log-loss confidence sets and jointly selects arm pairs to balance optimism and informative exploration. We establish a first-order regret bound that, in contrast with what previous results suggest, demonstrates that learning with preference feedback is as statistically efficient as learning from direct reward observation. Finally, we corroborate our theoretical findings with empirical evaluations against competitive baselines.

Dexterous grasping is the foundational primitive in embodied AI, demanding massive data to train robust models. As real-world data collection is expensive, simulation has become the mainstream paradigm. Yet, while cluttered scenes best reflect real-world applications, learning to grasp within them is bottlenecked by a critical scarcity of large-scale data. To resolve this, we curate high-quality 3D objects and supporting bases, proposing a scalable seed-and-filter strategy that bypasses sluggish scene-level optimization. This yields an unprecedented benchmark comprising over 2.6 million scenes and 0.4B scene-specific grasp ground truths, featuring diverse realistic layouts paired with rich semantic and geometric observations. Furthermore, we introduce the OmniDex model to overcome the grasp multimodality and last-millimeter precision errors plaguing current generative models. By coupling Soft Winner-Takes-All learning with human-inspired physical constraints during training, and utilizing physics-driven ranking, our approach achieves robust dexterous grasping without the latency of post-optimization. Experimental results show that OmniDex model achieves state-of-the-art performance and strong generalization across diverse scenes, views, and unseen objects.

Extreme ocean phenomena are challenging not only to predict but to diagnose, as accurate forecasts alone do not reveal the underlying physical drivers. While recent machine learning approaches achieve strong predictive skill, they remain largely opaque and provide limited guarantees of fidelity to ground-truth physics. We introduce OceanCBM, the first concept bottleneck model (CBM) for spatiotemporal prediction and mechanistic interrogation of ocean dynamics. OceanCBM uses mixed supervision to predict mixed layer heat content, a key precursor of marine heatwaves, while routing information through an intermediate layer of prescribed concepts derived from geophysical fluid dynamics and a 'free' concept. This design imposes soft physical structure without over-constraining the model, and the free concept both regularizes concept predictions and captures residual physical processes. Across ensemble initializations, we show that mixed supervision yields consistent mechanistic representations, whereas prediction-only and prescription-only baselines learn highly variable latent structures despite similar predictive performance. OceanCBM achieves interpretable, physically grounded representations without sacrificing skill, explicitly characterizing the interpretability-performance trade-off.

Irregular data assimilation is difficult because sparse, off-grid observations do not constrain the same state corrections from one cycle to the next. As the observation geometry changes, the set of supported correction directions changes as well. Many learning-based DA methods infer updates in a fixed latent or control space, even when the current observation layout supports a different set of correction directions. To address this mismatch, we introduce Observability-Constrained DataAssimilation with Control-Space Inference (ObsConDA), which determines those supported correction directions from the current background and observation geometry and infers only their control coefficients. On real surface-station assimilation, ObsConDA gives the best held-out station accuracy and the best full-field reconstruction among the tested classical and learned baselines. The same advantage carries to matched synthetic observations, explicit geometry shifts, and synthetic dynamical systems, supporting the view that the usable correction directions must change from cycle to cycle. Ablations show that the gain comes from adapting those directions themselves rather than from adding a latent corrector alone.

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.

Demand-side flexibility, i.e., forecasting, shifting, and curtailing residential energy loads, depends on thermal models trusted across millions of heterogeneous buildings. Existing tools force a hard tradeoff: high-fidelity physics simulators such as EnergyPlus are accurate but sequential and require per-building calibration, while purely data-driven sequence models scale but abandon the physical structure that makes their predictions trustworthy. We introduce NeuralBES (Building Energy Simulation), a differentiable emulator that resolves this tradeoff by parameterizing a resistance--capacitance (RC) based thermal model with a shared neural encoder: static building metadata such as floor area, vintage, and HVAC type is mapped to physically bounded capacitances, conductances, and equipment coefficients, which become the coefficients of a scalar linear recurrence solved via a log-space parallel scan, and a predictor--corrector loop closes the thermostat--temperature nonlinearity while preserving full-horizon gradient flow. Trained on the ResStock dataset across three climate zones, NeuralBES handles heterogeneous building archetypes, vintages, and climate zones within a single trained encoder, while black-box baselines produce statistically plausible but physically inconsistent trajectories. On the annual full-year rollout, NeuralBES is the only data-conditioned model that is simultaneously physics-valid and accurate to within 4 MAPE points of the strongest raw-error baseline, while operating at roughly an order of magnitude fewer parameters than the transformer and recurrent baselines; among physics-valid baselines at parameter parity it more than halves the MAPE of the grey-box RC alternative.

Generating clinical reports that summarize abnormal patterns, diagnostic findings, and clinical interpretations from long-term EEG recordings remains labor-intensive. We present CELM, the first clinical EEG-to-Language foundation model capable of summarizing long-duration, variable-length EEG recordings and performing end-to-end clinical report generation at multiple scales. CELM integrates pretrained EEG foundation models with language models to enable scalable multimodal learning. We curate a large-scale clinical EEG dataset containing 9,922 reports paired with approximately 11,000 hours of EEG recordings from 9,048 patients to train CELM, and release the benchmark with an automated report-structuring pipeline to facilitate future research. Experimental results show that CELM consistently outperforms existing methods across all evaluation settings. Importantly, we further conduct human evaluation with clinical experts, demonstrating that CELM generates reports that are more clinically coherent, diagnostically reliable, and better aligned with expert interpretation. We release our model and benchmark construction pipeline at https://anonymous.4open.science/r/CELM-3AF4.

Partial differential equations (PDEs) are central to modeling physical and engineering systems, but repeatedly solving parametric PDEs remains computationally expensive. Operator learning enables fast surrogate inference, yet typically requires large input–output paired datasets generated by costly high-fidelity PDE solvers. Unsupervised operator learning frameworks alleviate data dependency but remain hindered by computational bottlenecks. To address this, we propose Neural Variational Quantum Linear Solver (NVQLS), the first hybrid quantum–classical operator learning framework leveraging the Legendre-Galerkin weak formulation. We critically resolve the sign ambiguity in VQLS energy minimization, preventing erroneous solution representations. Additionally, we introduce a neural embedding, a novel encoding scheme to map varying forcings and PDE coefficients into parameterized quantum circuit representations. These structural innovations provide theoretical computational complexity advantages under efficient state preparation schemes, while achieving superior accuracy compared to a representative classical baseline. Validations on 1D and 2D parametric PDEs under diverse boundary conditions demonstrate NVQLS's capability to simultaneously process varying inputs, offering a scalable unsupervised approach to quantum-enhanced operator learning.