NeurIPS 2026 论文列表

Conference on Neural Information Processing Systems

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6,437篇论文

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When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective

Yuandong Cao, Chi C So, Jun-Min Wang, He Wang

展开摘要

Physics-informed neural networks (PINNs) are powerful surrogates for differential equations but are notoriously difficult to train due to spectral bias, stiffness, and poor accuracy on high-frequency or multiscale solutions. Adversarial training based on generative adversarial networks (GANs) has recently gained surprisingly strong empirical results in improving training, but the underlying mechanisms remain elusive. To this end, we propose a new analysis framework for adversarially trained PINNs, based on the key observation of how the discriminator in GANs can influence the training dynamics of PINNs. The framework first provides a much needed theoretical grounding to why and when adversarial training is effective in PINNs, then presents a unified analysis of GANs variants in such training, and finally leads to a new, practical, efficient training algorithm for PINNs. Empirical results demonstrate that our method can significantly reduce the pathology of PINNs training, thereby providing better models with superior performances, often several magnitudes more accurate than alternative methods.

Poster
WebSpline: Structure-Informed Splines for Real-Time 3D Gaussians from Monocular Videos

Jongmin Park, Jeonghwan Yun, Minh-Quan V Bui, Munchurl Kim

展开摘要

Dynamic scene reconstruction from monocular videos remains highly challenging, as existing methods often struggle to balance global structural coherence and local fine-grained details under limited multi-view cues. To address this challenge, we propose WebSpline, a novel dynamic 3D Gaussian framework that enables structurally coherent and high-fidelity reconstruction from monocular videos with fast rendering. The core of WebSpline is the Structure-Informed Spline (SIS) representation, which models each dynamic Gaussian trajectory using a learnable cubic Hermite spline whose motion is structurally organized with an auxiliary Structural Proxy Graph (SPG). The proposed framework is optimized in two stages: (i) in the first stage, the SPG is initialized from 2D point tracks and refined with temporal rigidity regularization to establish structural coherence for moving objects across the sequence; and (ii) in the second stage, the SIS representation is initialized from the refined SPG and optimized under both spatial and structural neighborhood constraints. At inference, Gaussian motion is obtained solely by evaluating the learned SIS, enabling fast rendering. Extensive experiments on the challenging monocular dynamic scene benchmarks, iPhone and NVIDIA, demonstrate that our WebSpline achieves state-of-the-art rendering quality while rendering over 10x faster than WorldTree, the second-best method on the iPhone dataset.

Poster
WavNAF: Learning Wave Propagation Priors for Neural Acoustic Fields

Taeho Kim, Hyunjun Kim, MinKyu Lee, SuBeen Lee, Inkyu An, Jae-Pil Heo

展开摘要

Room acoustics modeling requires capturing intricate wave phenomena beyond direct sound propagation, including reflections, refractions, and diffractions. Recent neural acoustic synthesis methods have progressively incorporated richer scene representations and physics-informed priors, yet typically learn acoustic behavior without considering wave propagation dynamics, which inherently capture diffraction and interference phenomena. We propose WavNAF, a framework that bridges wave dynamics and neural acoustic modeling by leveraging Finite-Difference Time-Domain (FDTD) simulations, which solve the wave equation on discrete spatiotemporal grids to capture these phenomena. However, directly applying FDTD at full scale is computationally prohibitive under CFL stability constraints. Inspired by traditional acoustic scale models, WavNAF constructs a geometry-preserving, scaled digital replica from NeRF-derived scene geometry and acoustically probes it with temporally compressed FDTD simulation. The resulting pressure maps are encoded not as direct full-scale Room Impulse Response (RIR) estimates, but as compressed-domain wave signatures that provide the neural acoustic field with a structured inductive bias beyond static geometry. To bridge the mismatch between these scaled simulation features and full-scale acoustic responses, we introduce a Neural Acoustic Scaling Module that adaptively recalibrates pressure-map features at the feature level for full-scale RIR prediction. Experiments show that WavNAF yields consistent gains over prior neural baselines across standard acoustic metrics.

Poster
Unsupervised Physics Informed Decomposition of Incomplete Time-Resolved Spectroscopy

Tom Muir, Qifeng Liu, Mohammadrahim Kazemzadeh, William Mills, Ales Leonardis, Huabing Yin, Alexander Krull

展开摘要

Raman spectroscopy is often hindered by strong autofluorescence backgrounds, which are typically handled by waiting for fluorescence to bleach before recording the Raman spectrum. Here, we instead show that short, incomplete recordings of the bleaching process already contain enough information to recover the underlying Raman signal. We present the first unsupervised model that operates on short, incomplete, variable-length sequences of time-resolved spectra, decomposing them into Raman spectra and autofluorescence components while simultaneously removing measurement noise. Our VAE-based method simultaneously learns (i) a bank of fluorophore spectra comprising the baseline, (ii) a model of the measurement noise, and (iii) the distribution of Raman spectra and decay behavior. We evaluate our method on spectral reconstruction and downstream peak detection, where it outperforms state-of-the-art approaches on multiple simulated benchmarks as well as on a newly collected real-world dataset of spectral time series. We further show that fluorescence decay dynamics themselves contain discriminative information that may be exploited in future work.

Poster
Ultra Fast PDE Solving via Physics Guided Few-step Diffusion

Xiangrui Cindy Kong, Yueqi Wang, Haoyang Zheng, Weijian Luo, Guang Lin

展开摘要

Diffusion-based models have demonstrated impressive accuracy and generalization in solving partial differential equations (PDEs). However, they still face significant limitations, such as high sampling costs and insufficient physical consistency, stemming from their many-step iterative sampling mechanism and lack of explicit physics constraints. To address these issues, we propose \emph{Phys-Instruct}, a novel physics-guided distillation framework which (1) not only compresses a pre-trained diffusion PDE solver into a few-step generator via matching generator and prior diffusion distributions to enable rapid sampling, (2) but also enhances the physics consistency by explicitly injecting PDE knowledge through a PDE distillation guidance. Phys-Instruct is built upon a solid theoretical foundation, leading to a practical physics-constrained training objective that admits tractable gradients. Across five PDE benchmarks, Phys-Instruct achieves orders-of-magnitude faster inference while reducing PDE Error by more than 8$\times$ compared to state-of-the-art diffusion baselines. Moreover, the resulting unconditional student model functions as a compact prior, enabling efficient and physically consistent inference for various downstream conditional tasks. Our results indicate that Phys-Instruct is a novel, effective, and efficient framework for ultra-fast PDE solving powered by deep generative models.

Poster
Training-Free Cultural Alignment of Large Language Models via Persona Disagreement

Dao S Minh, Trung Kiet Huynh, Chi Nguyen Tran, Phu Quy Nguyen Lam, Phu Hoa Pham, Tuan Nguyen, The Anh Han, Long Tran-thanh

展开摘要

Large language models are increasingly deployed in decisions that require culture-dependent moral judgements, yet they answer as if the whole world thinks with a Western mindset. The Moral Machine experiment showed this is wrong at scale: 40 million judgments across 233 countries reveal that moral preferences are systematically structured by culture, and a model that ignores this variation does not merely underperform, but also imposes one society's intuitions on all others. Existing fixes do not scale to global deployment, as fine-tuning needs per-country preference data and GPU budgets, reward-guided decoding needs per-country reward models, and activation steering needs access to model internals that black-box APIs do not expose. In this work, we focus on this realistic inference-time regime, with no weight updates, no training data, and no internal access. The key observation is that within-country demographic disagreement, not consensus, is the steering signal. When culturally grounded personas agree, the base model is already calibrated. But when they disagree, the spread tells us what to fix and how. We propose DISCA (Disagreement-Informed Steering for Cultural Alignment), which instantiates each country as a panel of four World-Values-Survey-grounded persona agents, converts their disagreement into a bounded, loss-averse correction whose magnitude is set by the panel's variance, and shrinks the correction toward zero when the estimate is unreliable. Across 20 countries and 7 open-weight backbones (2B–70B) from five model families, DISCA reduces cultural misalignment on MultiTP by 10–24% on binary moral dilemmas and 2–7% on open-ended scenarios. Furthermore, a smaller 14B backbone with DISCA reaches lower absolute misalignment than a vanilla 70B model.

Poster
The Subjectivity of Monoculture

Nathanael Jo, Nikhil Garg, Manish Raghavan

展开摘要

Machine learning models—including large language models (LLMs)—are often said to exhibit *monoculture*, where outputs agree strikingly often. However, we present two experiments that substantially disagree with prior findings of monoculture. In particular, we find that monoculture virtually disappears in one dataset when we include item difficulty compared to previous works that do not. Informed by these findings, we theoretically formalize what it means to measure monoculture. We show that monoculture is inherently subjective, relying on two key decisions: 1) the baseline null model for what "independence" should look like; and 2) the population of models and items under consideration. We conclude with concrete guidelines for future evaluators to ensure the robustness of their results.

Poster
SpikeSSL: A Universal Spike Inference Framework with Dynamics-Informed State-Space Layers

Chenghao Yue, Siming Xing, Shuran Liu, Angran Li, Yuanlong Zhang

展开摘要

Two-photon calcium imaging is a standard tool for recording large neural populations in vivo, yet inferring spikes accurately across the growing diversity of calcium indicators remains an open problem. Existing supervised methods achieve reasonable in-domain accuracy but generalize poorly to unseen indicators, because different indicators induce distinct fluorescence kinetics and signal statistics while existing architectures remain relatively simple generic temporal regressors without dynamics-matched inductive bias. We propose SpikeSSL, a universal spike inference framework whose temporal backbone is a bank of bidirectional IIR state-space layers broadly motivated by calcium dynamics. A multi-modal conditioning encoder maps indicator identity, sampling rate, and trace-level signal statistics into a global conditioning vector that modulates the backbone via Adaptive Layer Normalization, while a heteroscedastic variance head provides calibrated per-frame uncertainty. On a benchmark with five fixed evaluation splits built from 33 public ground-truth datasets, SpikeSSL achieves state-of-the-art performance in both in-domain and zero-shot leave-one-indicator-out settings. We also develop a biophysical simulation pipeline capable of generating paired fluorescence-spike traces with systematically varied kinetic parameters, spike statistics, response nonlinearities, baseline drift, and noise. Using this pipeline, we synthesize approximately 11{,}000 simulated traces. Augmenting training with these data effectively closes the cross-indicator domain gap and improves zero-shot generalization.

Poster
Sparsely-Supervised Data Assimilation via Physics-Informed Schrödinger Bridge

Dohyun Bu, Chanho Kim, Seokun Choi, Jong-Seok Lee

展开摘要

Data assimilation (DA) for systems governed by partial differential equations (PDE) aims to reconstruct full spatiotemporal fields from sparse high-fidelity (HF) observations while respecting physical constraints. While full-grid low-fidelity (LF) simulations provide informative priors in multi-fidelity settings, recovering an HF field consistent with both sparse observations and the governing PDE typically requires per-instance test-time optimization, which becomes a major bottleneck in time-critical applications. To alleviate this, amortized reconstruction using generative models has recently been proposed; however, such approaches rely on full-field HF supervision during training, which is often impractical in real-world settings. From a more realistic perspective, we propose the *Physics-Informed Conditional Schrödinger Bridge* (**PICSB**), which transports an informative LF prior toward an auxiliary-energy-defined, observation-conditioned HF endpoint law without any additional inference-time guidance. To enable learning without HF endpoints, **PICSB** employs an iterative surrogate-endpoint refresh scheme, and directly incorporates PDE residuals into the training objective while enforcing observations via hard conditioning throughout sampling. Experiments on fluid PDE benchmarks demonstrate that **PICSB** enables extremely fast spatiotemporal field reconstruction while achieving strong accuracy under sparse HF supervision.

Poster
Simplifying Transformer-Based U-Net Neural Physics Simulators

Pietro Sittoni, Francesco Tudisco

展开摘要

U-Net--style architectures are widely adopted for modeling physical systems, as their multiscale structure enables efficient processing of high-resolution data while reflecting the hierarchical structure of many physical phenomena. The most successful U-Net-based neural physics simulators often combine convolutions, Fourier layers, or specialized transformer mechanisms such as windowed or axial attention; however, these structured components can limit adaptability across different spatial and spatiotemporal dimensions. In this work, we revisit transformer-based U-Nets with the goal of simplifying attention-based neural physics simulators without sacrificing multiscale efficiency or predictive accuracy. We introduce \texttt{UFlex}, a simple attention-based U-Net whose blocks are obtained through only minimal modifications to standard self-attention, allowing the same architecture to be applied across one-, two-, three-dimensional, and spatiotemporal regular-grid problems without major design changes. Evaluated on seven challenging benchmarks (four 2D and three 3D), \texttt{UFlex} scales to resolutions of up to $512 \times 512$ in 2D and $256 \times 128 \times 256$ in 3D, while reducing training memory and accelerating training compared to state-of-the-art transformer baselines, all while achieving state-of-the-art predictive accuracy.

Poster
Self-Supervised Doppler-Guided RF Odometry

Kunzhe Song, Jialuo Du, Jingkai Lin, Huacheng Zeng

展开摘要

Accurate RF odometry remains difficult due to multipath interference, geometric degeneracy, and dynamic clutter. Existing approaches mitigate these challenges by relying on auxiliary sensors or ground-truth pose supervision, which limits scalability and deployability. We present RFWalk, a self-supervised, RF-only odometry framework that learns cross-frame correspondence without any pose annotations or auxiliary sensors. Our key insight is to cast each range-azimuth cell as a node in a space-time graph and recover inter-frame motion by learning a soft transition matrix through cycle-consistent contrastive random walks. To resolve geometric degeneracy in feature-poor scenes, we further introduce a physics-informed Doppler consistency loss that enforces agreement between the correspondence-induced displacement field and measured radial velocities. Experiments on challenging scenes show that RFWalk achieves competitive accuracy in static environments and substantially outperforms existing approaches in dynamic scenes.

Poster
SKIM: Pruning Large Language Model Agents via Selective Knowledge Informed Masking

Moonseok Choi, Giung Nam, Jongwon Jeong, Minki Kang, Juho Lee

展开摘要

Large Language Model (LLM) agents are increasingly deployed under structured generation, where grammar constraints enforce output format at inference time. Whereas existing compression methods target unconstrained generation, we first identify a fundamental mismatch: under structured generation, grammar constraints reduce the model's output distribution to valid tokens, and the logits matter most at the small set of positions that decide the agent's action. Motivated by this finding, we propose SKIM (Selective Knowledge-Informed Masking), the first pruning and distillation framework for LLM agents under structured generation, with both stages guided by token role. SKIM partitions token positions into context, decision, and format categories that reflect the input the model reads, the constrained options it chooses among, and the format realized by the constraint mechanism. Specifically, this partition drives two complementary axes: (1) category-aware pruning saliency scores that preserves parameters most relevant for decision positions; and (2) an on-policy distillation objective that aligns student and teacher on valid tokens, paired with category-aware feature matching. We evaluate SKIM on tool-calling benchmarks and within multi-step agent loops, across multiple model scales and sparsity levels. SKIM consistently improves accuracy over baselines, with its superiority becoming most striking in high-sparsity regimes where conventional methods struggle, demonstrating the potential of category-aware compression for deployment-time grammar-constrained agents.

Poster
ReGuidance: Diffusion Steering with Strong Latent Initializations Solves Hard Inverse Problems

Aayush Karan, Kulin Shah, Sitan Chen

展开摘要

In recent years there has been a flurry of activity around using pretrained diffusion models as informed data priors for solving inverse problems, and more generally around steering these models towards certain reward models. Training-free methods like gradient guidance have offered simple, flexible approaches for these tasks, but when the reward is not informative enough, e.g., in inverse problems with highly compressive measurements, these techniques can veer off the data manifold, failing to produce realistic data samples. To address this challenge, we devise a simple algorithm, *ReGuidance*, that leverages prior methods' solutions as strong initializations and substantially enhancing their realism. Given a candidate solution $x$ produced by a given method, we propose inverting the solution by running the unconditional probability flow ODE in reverse starting from $x$, and then using the resulting latent as an initialization for a deterministic steering process. Empirically, we evaluate our algorithm on difficult image restoration tasks including large box inpainting, heavily downscaled superresolution, and high noise deblurring with both linear and nonlinear blurring operations. We find that, using a wide range of baseline methods as initializations, applying our method results in much stronger samples with better realism and measurement consistency. We complement these results with rigorous proofs in commonly studied theoretical settings showing our technique boosts the reward and brings $x$ closer to the data manifold.

Poster
REINS: Learning Inertia-Induced Geometry for Physics-Consistent Motion Representation in Clinical Gait Phenotyping

Yiran Ding, Yufei Zhang, Zijun Cui

展开摘要

Parkinson's disease and other gait-related neurological disorders manifest in subtle but biomechanically meaningful changes in how patients move, making computational gait phenotyping a valuable tool for clinical assessment. Yet existing latent representations of motion are typically learned from data alone and miss the biomechanical structure that gives clinical motion its diagnostic meaning, leaving them vulnerable when training cohorts are small or acquisition sites differ. We propose REINS (Riemannian Embedding for INertia-induced motion Spaces), an Euler-Lagrange-induced motion representation that uses the generalized inertia matrix of articulated systems to define a biomechanically grounded geometry on configuration space. Because kinetic energy is itself a quadratic form in velocity weighted by the inertia matrix, this metric is a mechanically determined Riemannian structure, and we learn a latent embedding of the resulting structured space. By defining the representation space itself through rigid-body dynamics rather than enforcing physics as a post-hoc penalty, REINS aligns the geometry of motion representation with the same physical laws clinicians rely on to interpret gait. We apply the framework on Parkinson's disease gait analysis, where deviation from healthy motion is measured as a geodesic distance under the inertia-induced metric, and report results on healthy-control vs.\ PD discrimination and UPDRS-gait severity correlation.

Poster
RAWild: Toward Sensor-Agnostic RAW Object Detection via Physics-Guided Curve and Grid Modeling

Shuhong Liu, Gengjia Chang, Jun Liu, Xuangeng Chu, Yinqiang Zheng, Tatsuya Harada, Ziteng Cui

展开摘要

Camera sensor RAW data offers intrinsic advantages for object detection, including richer bit depth, preserved physical information, and freedom from image signal processor (ISP) distortions. However, varying exposure conditions, spectral sensitivities, and bit depths across devices introduce substantially larger domain gaps than sRGB, making sensor-agnostic generalization a fundamental challenge. In this study, we present a physics-guided global-local tone mapping framework for sensor-agnostic RAW object detection. By factoring sensor-induced variations into a global tonal correction and a spatially adaptive local color adjustment, both driven by RAW distribution priors, our framework enables a single network to train jointly across heterogeneous sensors. To further support cross-sensor generalization, we construct a physics-based RAW simulation pipeline that synthesizes realistic sensor outputs spanning diverse spectral sensitivities, illuminants, and sensor non-idealities. Extensive experiments across multiple RAW benchmarks, covering bit depths from 12 to 24, demonstrate state-of-the-art (SOTA) performance in single-dataset, mixed-dataset, and challenging robustness settings.

Poster
Prior Text-Informed Gate Attention Framework for Multimodal Psychiatric Disorder Diagnosis

Wensheng Zhai, Kaizhong Zheng, Difei Mei, Badong Chen, Liangjun Chen

展开摘要

Diagnosis of psychiatric disorders from functional magnetic resonance imaging (fMRI) is hindered by low-resource phenotypes, high inter-subject variability, and weakly interpretable multimodal fusion. We propose a prior text-informed gated attention framework (PTGA) that converts region-of-interest (ROI) level neuroimaging measures into statistically grounded textual priors via percentile-based soft binning. PTGA combines hemodynamic response function (HRF) aware spatiotemporal encoding with static graph topology modeling, and unifies variable-length fMRI time series through masked global temporal aggregation. It further uses text semantics as an inductive bias for prior-guided gated fusion, improving robustness under cross-modal noise. We compare PTGA with eight strong graph and multimodal baselines under a unified protocol. PTGA achieves up to 10.46\% and 8.01\% absolute improvements in autism spectrum disorder (ASD) and major depressive disorder (MDD) diagnosis, respectively, outperforming SOTA baselines. The learned gating also provides biologically plausible evidence: MDD related signals are concentrated in sensorimotor/visual/default-mode systems, while ASD related evidence is centered on the cerebellar network with joint contributions from default-mode, limbic, and dorsal-attention networks.

Poster
PolarScale: A Physics-Grounded Benchmark for Radiometrically Consistent RGB-to-Stokes Estimation

Beibei Lin, Tingting Chen, Xin Zhang, Wenhao Zhao, Dongjun Li, Zifeng Yuan

展开摘要

Polarization imaging provides rich physical cues beyond RGB imaging, yet acquiring such information typically requires specialized polarization-sensitive hardware that increases system cost and deployment complexity. Recent methods have proposed to infer polarization information directly from standard RGB images, providing a hardware-free alternative. While useful for describing relative polarimetric structure, these representations do not fully assess whether estimated images preserve the radiometric scale and intensity-dependent physical information needed for full Stokes reconstruction. To address this limitation, we introduce PolarScale, a physics-grounded benchmark for radiometrically consistent RGB-to-Stokes estimation. Instead of treating polarization inference from RGB images as conventional image-to-image translation, PolarScale evaluates how scale-independent descriptors, scale-dependent Stokes components, and radiometric scale jointly support physically meaningful Stokes reconstruction. Building upon this formulation, we propose three prediction strategies, namely direct, joint, and decoupled prediction, to study how scale-independent and scale-dependent polarimetric cues should be modeled across representative restoration-based and generative frameworks. Our analysis reveals that restoration-based frameworks outperform generative ones for radiometrically consistent polarization estimation (e.g., 28.61 vs. 26.14 dB PSNR). Furthermore, we find that jointly modeling scale-independent and scale-dependent parameters yields more stable physical representations than direct scale-dependent prediction (e.g., 28.61 vs. 26.81 dB PSNR). Overall, PolarScale provides a physics-grounded benchmark foundation for evaluating whether vision models can recover radiometrically consistent polarimetric signals from standard RGB images.

Poster
Physics-Informed Video Generation via Mixture-of-Experts Latent Alignment

Cong Wang, Hanxin Zhu, Jiayi Luo, Yonglin Tian, Xiaoqian Cheng, Peiyan Tu, Xin Jin, Long Chen, Zhibo Chen

展开摘要

Large-scale video generation models have made remarkable progress in semantic consistency and visual quality, producing videos that are increasingly coherent and visually convincing. Nevertheless, the dynamics induced by pixel-level fitting do not naturally accommodate the regularities that govern real-world motion and interaction, resulting in persistent shortcomings in physical plausibility. To address this limitation, we propose **PILA** (Physics-Informed Latent Alignment), a framework that injects physics-structured latent guidance into the frozen flow-matching dynamics of pretrained video models. Specifically, PILA first employs anchored field estimation to map frozen-generator latents into an operational physical attribute bank organized by field-proxy slots, using observable motion as a kinematic anchor for constructing less directly observed proxies. To handle the heterogeneity of real-world dynamics, PILA adopts a mixture-of-experts design over physical categories. Label-prior masked expert routing selects category-specific operator experts, whose refinements are regularized by operational residuals abstracted from physical relations. Finally, the refined proxies are fused into the physical attribute bank and decoded into a correction to the flow-matching vector field, injecting physics-aware guidance while preserving the visual prior of the pretrained backbone. With staged adapter training on Wan 2.1-1.3B and direct transfer of the learned adapter to Wan 2.2-14B, PILA achieves state-of-the-art results on VBench-2.0, VideoPhy-2, and PhyGenBench in both visual quality and benchmark-measured physical plausibility.

Poster
Physics-Informed Optimal Control by Control-Only Supervision with Error Guarantees on Value and Policy

Zihua Wang, Xiaopei Jiao, YUNFENG CAI

展开摘要

We propose a physics-informed method for solving high-dimensional optimal control problems that requires only control labels, not value function labels. A neural network parameterizes the value function, and the control policy is derived from its gradient. The network is trained by minimizing a weighted sum of the standard Hamilton–Jacobi–Bellman (HJB) residual and the mismatch between the network’s control output and control labels, which are precomputed by a state-dependent Riccati equation (SDRE) solver. Theoretically, with the help of the viscous HJB equation, we establish error bounds for the value function and its gradient, providing a rigorous performance guarantee for the resulting policy. Numerical experiments show that the learned model accurately approximates the optimal value function, closely matches the cost-to-go of the SDRE reference, and yields a neural controller that is significantly faster while exhibiting excellent stability.

Poster
Physics-Informed Functional Tucker Method with RKHS Factors for Sparse Spatiotemporal Reconstruction

Zhengyang Liu, Jianguo Huang, Junxi Hu, Yucheng Mi, Haojie Cai, Wenxuan Shen, Zhikun Zhang, Renfeng Peng, Guangtao Zhang, Zhiqiang Liu

展开摘要

Reconstructing physical dynamics from sparse and irregular spatiotemporal observations is a fundamental challenge in scientific research. However, sparsity leaves large regions of the field unconstrained, making the inverse problem ill-posed: a model may fit the observed sensors while producing nonphysical off-sensor structures or unreliable predictions between support times. To address this challenge, we propose PhysFTM---a physics-informed functional Tucker method that parameterizes Tucker mode factors in reproducing kernel Hilbert space (RKHS) and enforces governing physical laws through finite-difference residuals at collocation points. These physical constraints are essential for credible reconstruction, since most query locations are never directly supervised by data. Specifically, PhysFTM first reconstructs continuous spatial fields at observed times via an alternating minimization scheme, with separate treatments for the Tucker core tensor and the RKHS-based factors. To further enable continuous temporal resolution, PhysFTM constructs a continuous trajectory in Tucker-core space, which is decoded by the learned spatial RKHS-FTM representation to recover the full spatiotemporal field at arbitrary query times. Experiments on Allen--Cahn and Navier--Stokes with varying observation ratios demonstrate that PhysFTM achieves superior reconstruction accuracy, improved physical consistency, and stronger continuous-time modeling capability.

Poster