# Test-time Generalization for Physics through Neural Operator Splitting

arXiv: https://arxiv.org/abs/2602.00884 · HTML: https://mlsanity.com/paper/2602.00884/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 30 of 33)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [Multiple Physics Pretraining for Physical Surrogate Models](https://mlsanity.com/paper/2310.02994/) (2023)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [A Mathematical Guide to Operator Learning](https://mlsanity.com/paper/2312.14688/) (2023)
- [APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs](https://mlsanity.com/paper/2411.00180/) (2024)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [Walrus: A Cross-Domain Foundation Model for Continuum Dynamics](https://mlsanity.com/paper/2511.15684/) (2025)
- [Self-Supervised Learning with Lie Symmetries for Partial Differential Equations](https://mlsanity.com/paper/2307.05432/) (2023)
- [VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction](https://mlsanity.com/paper/2411.16063/) (2024)
- [Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos](https://mlsanity.com/paper/2503.18731/) (2025)
- [DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction](https://mlsanity.com/paper/2504.19496/) (2025)
- [Zebra: In-Context Generative Pretraining for Solving Parametric PDEs](https://mlsanity.com/paper/2410.03437/) (2024)
- [Interpretable Meta-Learning of Physical Systems](https://mlsanity.com/paper/2312.00477/) (2023)
- [Neural Context Flows for Meta-Learning of Dynamical Systems](https://mlsanity.com/paper/2405.02154/) (2024)

## Built on by (most cited first, 10 of 10)

- [Emergent Transfer of a Physics Foundation Model from Simulation to Laboratory Turbulence](https://mlsanity.com/paper/2606.01470/) (2026)
- [HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEs](https://mlsanity.com/paper/2605.00820/) (2026)
- [Unsupervised Adaptation of PDE Foundation Models](https://mlsanity.com/paper/2608.07053/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Kastor: An efficient fine-tuning strategy for generative emulation of PDE simulations](https://mlsanity.com/paper/2608.06107/) (2026)
- [Learnable composition for neural operators](https://mlsanity.com/paper/2609.03069/) (2026)
- [Into the danger zone: stable extrapolation in high-dimensional function and operator learning](https://mlsanity.com/paper/2609.36709/) (2026)
- [Cross-Domain Pretraining for Steady-State Neural CFD Surrogates](https://mlsanity.com/paper/2610.10398/) (2026)
- [Transferability of Learned States in Neural PDE Solvers](https://mlsanity.com/paper/2610.10972/) (2026)
- [SPLICE: Sparse Physics Library Identification and Compositional Expansion](https://mlsanity.com/paper/2610.17029/) (2026)

## Abstract (arXiv)

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 require 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.