Learning Neural Operators from Partial Observations via Latent Autoregressive Modeling

• URL: http://arxiv.org/abs/2601.15547v2
• Date: Tue, 27 Jan 2026 12:52:58 GMT
• Title: Learning Neural Operators from Partial Observations via Latent Autoregressive Modeling
• Abstract summary: We introduce the first systematic framework for learning neural operators from partial observation.<n>Our proposed Latent Autoregressive Neural Operator(LANO) introduces two novel components designed explicitly to address the core difficulties of partial observations.
• Score: 25.277110071740953
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of computational efficiency and accuracy, their underlying assumption of fully-observed spatial inputs severely restricts applicability in real-world applications. We introduce the first systematic framework for learning neural operators from partial observation. We identify and formalize two fundamental obstacles: (i) the supervision gap in unobserved regions that prevents effective learning of physical correlations, and (ii) the dynamic spatial mismatch between incomplete inputs and complete solution fields. Specifically, our proposed Latent Autoregressive Neural Operator(LANO) introduces two novel components designed explicitly to address the core difficulties of partial observations: (i) a mask-to-predict training strategy that creates artificial supervision by strategically masking observed regions, and (ii) a Physics-Aware Latent Propagator that reconstructs solutions through boundary-first autoregressive generation in latent space. Additionally, we develop POBench-PDE, a dedicated and comprehensive benchmark designed specifically for evaluating neural operators under partial observation conditions across three PDE-governed tasks. LANO achieves state-of-the-art performance with 18--69$\%$ relative L2 error reduction across all benchmarks under patch-wise missingness with less than 50$\%$ missing rate, including real-world climate prediction. Our approach effectively addresses practical scenarios involving up to 75$\%$ missing rate, to some extent bridging the existing gap between idealized research settings and the complexities of real-world scientific computing.

Related papers

• SpaceEra++: A Unified Framework Towards 3D Spatial Reasoning in Video [88.79625979053873]
  We propose a novel framework, SpaceEra, for pre-trained vision-language models (VLMs)<n>We extend the original framework into a comprehensive system, termed SpaceEra++, which spans data construction, model design, training optimization, and prompting inference.<n>In addition, to enhance spatial reasoning, we develop SpaceAlign, which enforces pairwise object constraints by jointly exploiting absolute coordinates and relative spatial relations.
  arXiv  Detail & Related papers  (2026-07-02T06:56:29Z)
• Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observations [3.523696436541849]
  Di-BiLPS is a unified neural framework that handles both forward and inverse PDE problems under extremely sparse observations.<n>It consistently achieves SOTA performance under extremely sparse inputs, while substantially reducing computational cost.<n>It enables zero-shot super-resolution, as it allows predictions over continuous spatial-temporal domains.
  arXiv  Detail & Related papers  (2026-05-13T17:11:07Z)
• Divide-and-Conquer Approach to Holistic Cognition in High-Similarity Contexts with Limited Data [73.20753799870282]
  We propose a novel Divide-and-Conquer Holistic Cognition Network (DHCNet)<n>DHCNet implements a divide-and-conquer strategy by decomposing holistic cues into spatially-associated subtle discrepancies.<n>DHCNet achieves remarkable performance on five widely-used Ultra-FGVC datasets.
  arXiv  Detail & Related papers  (2026-04-21T11:17:09Z)
• Constraints Matrix Diffusion based Generative Neural Solver for Vehicle Routing Problems [16.541111954252397]
  We propose a novel fusion neural network framework that employs a discrete noise graph diffusion model to learn the underlying constraints of vehicle routing problems.<n>This work represents the first comprehensive experimental investigation of neural network model solvers across a 378-combinatorial space.
  arXiv  Detail & Related papers  (2026-03-08T10:03:34Z)
• Sample-Efficient Neurosymbolic Deep Reinforcement Learning [49.60927398960061]
  We propose a neuro-symbolic Deep RL approach that integrates background symbolic knowledge to improve sample efficiency.<n>Online reasoning is performed to guide the training process through two mechanisms.<n>We show improved performance over a state-of-the-art reward machine baseline.
  arXiv  Detail & Related papers  (2026-01-06T09:28:53Z)
• Scale-aware Adaptive Supervised Network with Limited Medical Annotations [17.42211316792232]
  SASNet is a dual-branch architecture that leverages both low-level and high-level feature representations through novel scale-aware adaptive reweight mechanisms.<n>Our approach introduces three key methodological innovations, including the Scale-aware Adaptive Reweight strategy.<n> SASNet achieves superior performance with limited labeled data, surpassing state-of-the-art semi-supervised methods.
  arXiv  Detail & Related papers  (2026-01-02T23:55:17Z)
• LTD-Bench: Evaluating Large Language Models by Letting Them Draw [57.237152905238084]
  LTD-Bench is a breakthrough benchmark for large language models (LLMs)<n>It transforms LLM evaluation from abstract scores to directly observable visual outputs by requiring models to generate drawings through dot matrices or executable code.<n> LTD-Bench's visual outputs enable powerful diagnostic analysis, offering a potential approach to investigate model similarity.
  arXiv  Detail & Related papers  (2025-11-04T08:11:23Z)
• Physics-informed deep operator network for traffic state estimation [16.262431071606574]
  Traffic state estimation (TSE) fundamentally involves solving high-dimensional partial differential equations (PDEs) governing traffic flow dynamics from limited noisy measurements.<n>This paper adopts a physics-informed deep operator network framework that reformulates TSE as an operator learning problem.
  arXiv  Detail & Related papers  (2025-08-18T02:59:42Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEs [0.0]
  Deep operator network (DeepONet) has shown promise as surrogate models for systems governed by partial differential equations (PDEs)<n>In this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process.
  arXiv  Detail & Related papers  (2025-01-14T20:38:30Z)
• Reinforcement Learning under Latent Dynamics: Toward Statistical and Algorithmic Modularity [51.40558987254471]
  Real-world applications of reinforcement learning often involve environments where agents operate on complex, high-dimensional observations. This paper addresses the question of reinforcement learning under $textitgeneral$ latent dynamics from a statistical and algorithmic perspective.
  arXiv  Detail & Related papers  (2024-10-23T14:22:49Z)
• DeltaPhi: Physical States Residual Learning for Neural Operators in Data-Limited PDE Solving [54.605760146540234]
  DeltaPhi is a novel learning framework that transforms the PDE solving task from learning direct input-output mappings to learning the residuals between similar physical states.<n>Extensive experiments demonstrate consistent and significant improvements across diverse physical systems.
  arXiv  Detail & Related papers  (2024-06-14T07:45:07Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• Learning a Domain-Agnostic Visual Representation for Autonomous Driving via Contrastive Loss [25.798361683744684]
  Domain-Agnostic Contrastive Learning (DACL) is a two-stage unsupervised domain adaptation framework with cyclic adversarial training and contrastive loss. Our proposed approach achieves better performance in the monocular depth estimation task compared to previous state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-03-10T07:06:03Z)
• On Duality Gap as a Measure for Monitoring GAN Training [2.733700237741334]
  Generative adversarial network (GAN) is among the most popular deep learning models for learning complex data distributions. This paper presents a theoretical understanding of this limitation and proposes a more dependable estimation process for the duality gap.
  arXiv  Detail & Related papers  (2020-12-12T04:32:52Z)
• Improving Monocular Depth Estimation by Leveraging Structural Awareness and Complementary Datasets [21.703238902823937]
  We propose a structure-aware neural network with spatial attention blocks to exploit the spatial relationship of visual features. Second, we introduce a global focal relative loss for uniform point pairs to enhance spatial constraint in the prediction. Third, based on analysis of failure cases for prior methods, we collect a new Hard Case (HC) Depth dataset of challenging scenes.
  arXiv  Detail & Related papers  (2020-07-22T08:21:02Z)
• Local Propagation in Constraint-based Neural Network [77.37829055999238]
  We study a constraint-based representation of neural network architectures. We investigate a simple optimization procedure that is well suited to fulfil the so-called architectural constraints.
  arXiv  Detail & Related papers  (2020-02-18T16:47:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.