Test-time Generalization for Physics through Neural Operator Splitting

• URL: http://arxiv.org/abs/2602.00884v1
• Date: Sat, 31 Jan 2026 20:08:57 GMT
• Title: Test-time Generalization for Physics through Neural Operator Splitting
• Authors: Louis Serrano, Jiequn Han, Edouard Oyallon, Shirley Ho, Rudy Morel,
• Abstract summary: We introduce a neural operator splitting strategy that searches over compositions of training operators to approximate unseen dynamics.<n>Our approach achieves state-of-the-art zero-shot generalization results, while being able to recover the underlying PDE parameters.
• Score: 12.59844119790293
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen PDE coefficients or unseen physics. Prior works address this limitation with large-scale multiple physics pretraining followed by fine-tuning, but this still requires examples from the new dynamics, falling short of true zero-shot generalization. In this work, we propose a method to enhance generalization at test time, i.e., without modifying pretrained weights. Building on DISCO, which provides a dictionary of neural operators trained across different dynamics, we introduce a neural operator splitting strategy that, at test time, searches over compositions of training operators to approximate unseen dynamics. On challenging out-of-distribution tasks including parameter extrapolation and novel combinations of physics phenomena, our approach achieves state-of-the-art zero-shot generalization results, while being able to recover the underlying PDE parameters. These results underscore test-time computation as a key avenue for building flexible, compositional, and generalizable neural operators.

Related papers

• Learning Physical Operators using Neural Operators [10.57578521926415]
  We train neural operators to learn individual non-linear physical operators while approximating linear operators with fixed finite-difference convolutions.<n>We formulate the modelling task as a neural ordinary differential equation (ODE) where these learned operators constitute the right-hand side.<n>Our approach achieves better convergence and superior performance when generalising to unseen physics.
  arXiv  Detail & Related papers  (2026-02-26T15:27:14Z)
• Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equations [65.80144621950981]
  We build on Wiener chaos expansions (WCE) to design neural operator (NO) architectures for SPDEs and SDEs.<n>We show that WCE-based neural operators provide a practical and scalable way to learn SDE/SPDE solution operators.
  arXiv  Detail & Related papers  (2026-01-03T00:59:25Z)
• Accelerating PDE Solvers with Equation-Recast Neural Operator Preconditioning [9.178290601589365]
  Minimal-Data Parametric Neural Operator Preconditioning (MD-PNOP) is a new paradigm for accelerating parametric PDE solvers.<n>It recasts the residual from parameter deviation as additional source term, where trained neural operators can be used to refine the solution in an offline fashion.<n>It consistently achieves 50% reduction in computational time while maintaining full order fidelity for fixed-source, single-group eigenvalue, and multigroup coupled eigenvalue problems.
  arXiv  Detail & Related papers  (2025-09-01T12:14:58Z)
• From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing [0.0]
  The study covers foundational models such as Deep Operator Networks (DeepONet) and Principal Component Analysis-based Neural Networks (PCANet)<n>The review delves into applying neural operators as surrogates in Bayesian inference problems, showcasing their effectiveness in accelerating posterior inference while maintaining accuracy.<n>It outlines emerging strategies to address these issues, such as residual-based error correction and multi-level training.
  arXiv  Detail & Related papers  (2025-03-07T17:25:25Z)
• DimINO: Dimension-Informed Neural Operator Learning [41.37905663176428]
  DimINO is a framework inspired by dimensional analysis.<n>It can be seamlessly integrated into existing neural operator architectures.<n>It achieves up to 76.3% performance gain on PDE datasets.
  arXiv  Detail & Related papers  (2024-10-08T10:48:50Z)
• PICL: Physics Informed Contrastive Learning for Partial Differential Equations [7.136205674624813]
  We develop a novel contrastive pretraining framework that improves neural operator generalization across multiple governing equations simultaneously. A combination of physics-informed system evolution and latent-space model output are anchored to input data and used in our distance function. We find that physics-informed contrastive pretraining improves accuracy for the Fourier Neural Operator in fixed-future and autoregressive rollout tasks for the 1D and 2D Heat, Burgers', and linear advection equations.
  arXiv  Detail & Related papers  (2024-01-29T17:32:22Z)
• On the Dynamics Under the Unhinged Loss and Beyond [104.49565602940699]
  We introduce the unhinged loss, a concise loss function, that offers more mathematical opportunities to analyze closed-form dynamics. The unhinged loss allows for considering more practical techniques, such as time-vary learning rates and feature normalization.
  arXiv  Detail & Related papers  (2023-12-13T02:11:07Z)
• Neural Operators for Accelerating Scientific Simulations and Design [85.89660065887956]
  An AI framework, known as Neural Operators, presents a principled framework for learning mappings between functions defined on continuous domains. Neural Operators can augment or even replace existing simulators in many applications, such as computational fluid dynamics, weather forecasting, and material modeling.
  arXiv  Detail & Related papers  (2023-09-27T00:12:07Z)
• Long-time integration of parametric evolution equations with physics-informed DeepONets [0.0]
  We introduce an effective framework for learning infinite-dimensional operators that map random initial conditions to associated PDE solutions within a short time interval. Global long-time predictions across a range of initial conditions can be then obtained by iteratively evaluating the trained model. This introduces a new approach to temporal domain decomposition that is shown to be effective in performing accurate long-time simulations.
  arXiv  Detail & Related papers  (2021-06-09T20:46:17Z)
• What training reveals about neural network complexity [80.87515604428346]
  This work explores the hypothesis that the complexity of the function a deep neural network (NN) is learning can be deduced by how fast its weights change during training. Our results support the hypothesis that good training behavior can be a useful bias towards good generalization.
  arXiv  Detail & Related papers  (2021-06-08T08:58:00Z)
• Incorporating NODE with Pre-trained Neural Differential Operator for Learning Dynamics [73.77459272878025]
  We propose to enhance the supervised signal in learning dynamics by pre-training a neural differential operator (NDO) NDO is pre-trained on a class of symbolic functions, and it learns the mapping between the trajectory samples of these functions to their derivatives. We provide theoretical guarantee on that the output of NDO can well approximate the ground truth derivatives by proper tuning the complexity of the library.
  arXiv  Detail & Related papers  (2021-06-08T08:04:47Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)

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.