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Applications · Language, Speech and Dialog

Anikait Singh, Sheryl Hsu, Kyle Hsu, Eric Mitchell, Stefano Ermon, Tatsunori Hashimoto, Archit Sharma, Chelsea Finn

Effective personalization of LLMs is critical for a broad range of user-interfacing applications such as virtual assistants and content curation. Inspired by the strong in-context capabilities of LLMs, we propose few-shot preference optimization (FSPO), an algorithm for LLM personalization that reframes reward modeling as a meta-learning problem. Under FSPO, an LLM learns to quickly infer a personalized reward function for a user via a few labeled preferences. FSPO also utilizes user description rationalization (RAT) to encourage better reward modeling and instruction following, recovering performance with the oracle user description. Since real-world preference data is challenging to collect at scale, we propose careful design choices to construct synthetic preference datasets for personalization, generating over 1M synthetic personalized preferences using publicly available LLMs. To successfully transfer from synthetic data to real users, we find it crucial for the data to exhibit both high diversity and coherent, self-consistent structure. We evaluate FSPO on personalized open-ended generation for up to 1,500 synthetic users across three domains: movie reviews, education, and open-ended question answering. We also run a controlled human study. Overall, FSPO achieves an 87% Alpaca Eval win-rate in generating responses that are personalized to synthetic users and a 70% win-rate with real human users in open-ended question answering.

Applications · Physics

Bogdan Raonic, Siddhartha Mishra, Samuel Lanthaler

Data-driven models are increasingly adopted in critical scientific fields like weather forecasting and fluid dynamics. These methods can fail on out-of-distribution (OOD) data, but detecting such failures in regression tasks is an open challenge. We propose a new OOD detection method based on estimating joint likelihoods using a score-based diffusion model. This approach considers not just the input but also the regression model's prediction, providing a task-aware reliability score. Across numerous scientific datasets, including PDE datasets, satellite imagery and brain tumor segmentation, we show that this likelihood strongly correlates with prediction error. Our work provides a foundational step towards building a verifiable 'certificate of trust', thereby offering a practical tool for assessing the trustworthiness of AI-based scientific predictions.

Deep Learning · Graph Neural Networks

Atamert Rahma, Chinmay Datar, Ana Cukarska, Felix Dietrich

Learning dynamical systems that respect physical symmetries and constraints remains a fundamental challenge in data-driven modeling. Integrating physical laws with graph neural networks facilitates principled modeling of complex N-body dynamics and yields accurate and permutation-invariant models. However, training graph neural networks with iterative, gradient-descent-based optimization algorithms (e.g., Adam, RMSProp, LBFGS) often leads to slow training, especially for large, complex systems. In comparison to 15 different optimizers, we demonstrate that Hamiltonian Graph Networks (HGN) can be trained 150-600× faster - but with comparable accuracy - by replacing iterative optimization with random feature-based parameter construction. We show robust performance in diverse simulations, including N-body mass-spring and molecular dynamics systems in up to $3$ dimensions and 10,000 particles with different geometries, while retaining essential physical invariances with respect to permutation, rotation, and translation. Our proposed approach is benchmarked using a NeurIPS 2022 Datasets and Benchmarks Track publication to further demonstrate its versatility. We reveal that even when trained on minimal 8-node systems, the model can generalize in a zero-shot manner to systems as large as 4096 nodes without retraining. Our work challenges the dominance of iterative gradient-descent-based optimization algorithms for training neural network models for physical systems.

Computer Vision · Classification and Understanding

Bingxue Zhao, Qi Zhang, Hui Huang

Modeling realistic pedestrian trajectories requires accounting for both social interactions and environmental context, yet most existing approaches largely emphasize social dynamics. We propose EnvSocial-Diff: a diffusion-based crowd simulation model informed by social physics and augmented with environmental conditioning and individual-group interaction. Our structured environmental conditioning module explicitly encodes obstacles, objects of interest, and lighting levels, providing interpretable signals that capture scene constraints and attractors. In parallel, the individual-group interaction module goes beyond individual-level modeling by capturing both fine-grained interpersonal relations and group-level conformity through a graph-based design. Experiments on multiple benchmark datasets demonstrate that EnvSocial-Diff outperforms the latest state-of-the-art methods, underscoring the importance of explicit environmental conditioning and multi-level social interaction for realistic crowd simulation.

Chinmay Datar, Taniya Kapoor, Abhishek Chandra, Qing Sun, Erik L. Bolager, Iryna Burak, Anna Veselovska, Massimo Fornasier, Felix Dietrich

Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their accuracy and training speed are limited by two core barriers: gradient-descent-based iterative optimization over complex loss landscapes and non-causal treatment of time as an extra spatial dimension. We present Frozen-PINN, a novel PINN based on the principle of space-time separation that leverages random features instead of training with gradient descent, and incorporates temporal causality by construction. On nine PDE benchmarks, including challenges like extreme advection speeds, shocks, and high-dimensionality, Frozen-PINNs achieve superior training efficiency and accuracy over state-of-the-art PINNs, often by several orders of magnitude. Our work addresses longstanding training and accuracy bottlenecks of PINNs, delivering quickly trainable, highly accurate, and inherently causal PDE solvers, a combination that prior methods could not realize. Our approach challenges the reliance of PINNs on stochastic gradient-descent-based methods and specialized hardware, leading to a paradigm shift in PINN training and providing a challenging benchmark for the community.

Optimization · Non-Convex

Pranav Vaidhyanathan, Lucas Schorling, Natalia Ares, Michael Osborne

We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics. Previous algorithms, including the ubiquitous Adam, operate at the so-called adaptive edge of stability regime during training, leading to rapid oscillations and slowed convergence of loss. However, VRAdam adds a higher order penalty on the learning rate based on the velocity such that the algorithm automatically slows down whenever weight updates become large. In practice, we observe that the effective dynamic learning rate shrinks in high-velocity regimes, and damping oscillations. By combining this velocity‑based regularizer for global damping with Adam’s per‑parameter scaling, we create a powerful hybrid optimizer. For this optimizer, we provide rigorous theoretical analysis of operation at the edge of stability from a physical and control perspective for the momentum. Furthermore, we derive convergence bounds with the rate $\mathcal{O}(\ln(N)/\sqrt{N})$ for a stochastic non‑convex objective under mild assumptions. We demonstrate that VRAdam exceeds the performance against standard optimizers including AdamW. We benchmark various tasks such as image classification, language modeling, and generative modeling using diverse architectures and training methodologies including Convolutional Neural Networks (CNNs), Transformers, and GFlowNets.

Applications · Robotics

Yitian Zheng, Zhangchen Ye, Weijun Dong, Shengjie Wang, Yuyang Liu, Chongjie Zhang, Chuan Wen, Yang Gao

Recent advances in hierarchical robot systems leverage a high-level planner to propose task plans and a low-level policy to generate robot actions. This design allows training the planner on action-free or even non-robot data sources (e.g., videos), providing transferable high-level guidance. Nevertheless, grounding these high-level plans into executable actions remains challenging, especially with the limited availability of high-quality robot data. To this end, we propose to improve the low-level policy through online interactions. Specifically, our approach collects online rollouts, retrospectively annotates the corresponding high-level goals from achieved outcomes, and aggregates these hindsight-relabeled experiences to update a goal-conditioned imitation policy. Our method, Hindsight Flow-conditioned Online Imitation (HinFlow), instantiates this idea with 2D point flows as the high-level planner. Across diverse manipulation tasks in both simulation and physical world, our method achieves more than $2\times$ performance improvement over the base policy, significantly outperforming the existing methods. Moreover, our framework enables policy acquisition from planners trained on cross-embodiment video data, demonstrating its potential for scalable and transferable robot learning.

Applications · Robotics

Patrick Yin, Tyler Westenbroek, Zhengyu Zhang, Ignacio Dagnino, Eeshani Shilamkar, Numfor Mbiziwo-Tiapo, Simran Bagaria, Xinlei Liu, Galen Mullins, Andrey Kolobov 等

Reinforcement learning in massively parallel physics simulations has driven major progress in sim-to-real robot learning. However, current approaches remain brittle and task-specific, relying on extensive per-task engineering to design rewards, curricula, and demonstrations. Even with this engineering, they often fail on long-horizon, contact-rich manipulation tasks and do not meaningfully scale with compute, as performance quickly saturates when training revisits the same narrow regions of state space. We introduce \Method, a simple and scalable framework that enables on-policy reinforcement learning to robustly solve a broad class of dexterous manipulation tasks using a single reward function, fixed algorithm hyperparameters, no curricula, and no human demonstrations. Our key insight is that long-horizon exploration can be dramatically simplified by using simulator resets to systematically expose the RL algorithm to the diverse set of robot-object interactions which underlie dexterous manipulation. \Method\ programmatically generates such resets with minimal human input, converting additional compute directly into broader behavioral coverage and continued performance gains. We show that \Method\ gracefully scales to long-horizon dexterous manipulation tasks beyond the capabilities of existing approaches and is able to learn robust policies over significantly wider ranges of initial conditions than baselines. Finally, we distill \Method \ into visuomotor policies which display robust retrying behavior and substantially higher success rates than baselines when transferred to the real world zero-shot. Project webpage: https://omnireset.github.io

Applications · Physics

Shi Yin, Zujian Dai, Xinyang Pan, Lixin He

Deep learning methods for electronic-structure Hamiltonian prediction have offered significant computational efficiency advantages over traditional density functional theory (DFT), yet the diversity of atomic types, structural patterns, and the high-dimensional complexity of Hamiltonians pose substantial challenges to the generalization performance. In this work, we contribute on both the methodology and dataset sides to advance universal deep learning paradigm for Hamiltonian prediction. On the method side, we propose NextHAM, a neural E(3)-symmetry and expressive correction method for efficient and generalizable materials electronic-structure Hamiltonian prediction. First, we introduce the zeroth-step Hamiltonians, which can be efficiently constructed by the initial charge density of DFT, as informative input descriptors that enable the model to effectively capture prior knowledge of electronic structures. Second, we present a neural Transformer architecture with strict E(3)-symmetry and high non-linear expressiveness for Hamiltonian prediction. Third, we propose a novel training objective to ensure the accuracy performance of Hamiltonians in both real space and reciprocal space, preventing error amplification and the occurrence of ``ghost states'' caused by the large condition number of the overlap matrix. On the dataset side, we curate a broad-coverage large benchmark, namely Materials-HAM-SOC, comprising $17,000$ material structures spanning more than $60$ elements from six rows of the periodic table and explicitly incorporating spin–orbit coupling (SOC) effects, providing high-quality data resources for training and evaluation. Comprehensive experimental results demonstrate that NextHAM achieves excellent accuracy in predicting Hamiltonians and band structures, with spin-off-diagonal blocks reaching the accuracy of sub-$\mu$eV scale. These results establish NextHAM as a universal and highly accurate deep learning model for electronic-structure prediction, delivering DFT-level precision with dramatically improved computational efficiency.

Applications · Physics

Jeffrey Lai, Anthony Bao, William Gilpin

Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present Panda, Patched Attention for Nonlinear Dynamics. We train Panda on a novel synthetic, extensible dataset of 20,000 chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, Panda exhibits emergent properties: zero-shot forecasting of unseen chaotic systems preserving both short-term accuracy and distributional measures, nonlinear resonance patterns in attention heads, and effective prediction of real-world experimental time series. Despite having been trained only on low-dimensional ordinary differential equations, Panda spontaneously develops the ability to predict partial differential equations without retraining. We also demonstrate a neural scaling law for differential equations, underscoring the potential of pretrained models for probing abstract mathematical domains like nonlinear dynamics.

General Machine Learning · Representation Learning

Cindy Zhang, Elif Ertekin, Peter Orbanz, Ryan P Adams

Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invariance to specific symmetries typically requires designing bespoke architectures for each group of symmetries, limiting scalability and preventing knowledge transfer across related symmetries. In the case of the space groups—symmetries critical to modeling crystalline solids in materials science and condensed matter physics—this challenge is particularly salient as there are 230 such groups in three dimensions. In this work we present a new approach to crystallographic symmetries by developing a single machine learning architecture that is capable of adapting its weights automatically to enforce invariance to any input space group. Our approach is based on constructing symmetry-adapted Fourier bases through an explicit characterization of constraints that group operations impose on Fourier coefficients. Encoding these constraints into a neural network layer enables weight sharing across different space groups, allowing the model to leverage structural similarities between groups and overcome data sparsity when limited measurements are available for specific groups. We demonstrate the effectiveness of this approach in achieving competitive performance on material property prediction tasks and performing zero-shot learning to generalize to unseen groups.

Computer Vision · Image and Video Generation

Shilin Lu, Zhuming Lian, Zihan Zhou, Shaocong Zhang, Chen Zhao, Adams Kong

Image composition aims to seamlessly insert a user-specified object into a new scene, but existing models struggle with complex lighting (e.g., accurate shadows, water reflections) and diverse, high-resolution inputs. Modern text-to-image diffusion models (e.g., SD3.5, FLUX) already encode essential physical and resolution priors, yet lack a framework to unleash them without resorting to latent inversion, which often locks object poses into contextually inappropriate orientations, or brittle attention surgery. We propose SHINE, a training-free framework for Seamless, High-fidelity Insertion with Neutralized Errors. SHINE introduces manifold-steered anchor loss, leveraging pretrained customization adapters (e.g., IP-Adapter) to guide latents for faithful subject representation while preserving background integrity. Artifact-suppression guidance and adaptive background blending are proposed to further eliminate low-quality outputs and visible seams. To address the lack of rigorous benchmarks, we introduce ComplexCompo, featuring diverse resolutions and challenging conditions such as low lighting, strong illumination, intricate shadows, and reflective surfaces. Experiments on ComplexCompo and DreamEditBench show state-of-the-art performance on standard metrics (e.g., DINOv2) and human-aligned scores (e.g., DreamSim, ImageReward, VisionReward). Code is available at https://github.com/ZhumingLian/SHINE

Applications · Genetics, Cell Biology, Health, etc

Suyi Chen, Haibin Ling

As a critical modality for structural biology, cryogenic electron microscopy (cryo-EM) facilitates the determination of macromolecular structures at near-atomic resolution. The core computational task in single-particle cryo-EM is to reconstruct the 3D electrostatic potential of a molecule from noisy 2D projections acquired at unknown orientations. Gaussian mixture models (GMMs) provide a continuous, compact, and physically interpretable representation for molecular density and have recently gained interest in cryo-EM reconstruction. However, existing methods rely on external consensus maps or atomic models for initialization, limiting their use in self-contained pipelines. In parallel, differentiable rendering techniques such as Gaussian splatting have demonstrated remarkable scalability and efficiency for volumetric representations, suggesting a natural fit for GMM-based cryo-EM reconstruction. However, off-the-shelf Gaussian splatting methods are designed for photorealistic view synthesis and remain incompatible with cryo-EM due to mismatches in the image formation physics, reconstruction objectives, and coordinate systems. Addressing these issues, we propose **cryoSplat**, a GMM-based method that integrates Gaussian splatting with the physics of cryo-EM image formation. In particular, we develop an orthogonal projection-aware Gaussian splatting, with adaptations such as a view-dependent normalization term and FFT-aligned coordinate system tailored for cryo-EM imaging. These innovations enable stable and efficient homogeneous reconstruction directly from raw cryo-EM particle images using random initialization. Experimental results on real datasets validate the effectiveness and robustness of cryoSplat over representative baselines. The code will be released at https://github.com/Chen-Suyi/cryosplat.

Deep Learning · Generative Models and Autoencoders

Shaobin Zhuang, Zhipeng Huang, Ying Zhang, Fangyikang Wang, Canmiao Fu, Binxin Yang, Chong Sun, Chen Li, Yali Wang

GPT has shown its remarkable success in natural language processing. However, the language sequence is not sufficient to describe spatial-temporal details in the visual world. Alternatively, the video sequence is good at capturing such details. Motivated by this fact, we propose a concise Video-GPT in this paper by treating video as new language for visual world modeling. By analogy to next token prediction in GPT, we introduce a novel next clip diffusion paradigm for pretraining Video-GPT. Different from the previous works, this distinct paradigm allows Video-GPT to tackle both short-term generation and long-term prediction, by autoregressively denoising the noisy clip according to the clean clips in the history. Extensive experiments show our Video-GPT achieves the state-of-the-art performance on video prediction, which is the key factor towards world modeling (Physics-IQ Benchmark: Video-GPT 34.97 vs. Kling 23.64 vs. Wan 20.89). Moreover, it can be well adapted on 6 mainstream video tasks in both video generation and understanding, showing its great generalization capacity in downstream.

Applications · Chemistry and Drug Discovery

Zhanghan Ni, Yanjing Li, Zeju Qiu, Bernhard Schölkopf, Hongyu Guo, Weiyang Liu, Shengchao Liu

Generative models have recently advanced $\textit{de novo}$ protein design by learning the statistical regularities of natural structures. However, current approaches face three key limitations: (1) Existing methods cannot jointly learn protein geometry and design tasks, where pretraining can be a solution; (2) Current pretraining methods mostly rely on local, non-rigid atomic representations for property prediction downstream tasks, limiting global geometric understanding for protein generation tasks; and (3) Existing approaches have yet to effectively model the rich dynamic and conformational information of protein structures. To overcome these issues, we introduce $\textbf{RigidSSL}$ ($\textit{Rigidity-Aware Self-Supervised Learning}$), a geometric pretraining framework that front-loads geometry learning prior to generative finetuning. Phase I (RigidSSL-Perturb) learns geometric priors from 432K structures from the AlphaFold Protein Structure Database with simulated perturbations. Phase II (RigidSSL-MD) refines these representations on 1.3K molecular dynamics trajectories to capture physically realistic transitions. Underpinning both phases is a bi-directional, rigidity-aware flow matching objective that jointly optimizes translational and rotational dynamics to maximize mutual information between conformations. Empirically, RigidSSL variants improve designability by up to 43\% while enhancing novelty and diversity in unconditional generation. Furthermore, RigidSSL-Perturb improves the success rate by 5.8\% in zero-shot motif scaffolding and RigidSSL-MD captures more biophysically realistic conformational ensembles in G protein-coupled receptor modeling. The code is available at: https://github.com/ZhanghanNi/RigidSSL.git.

Applications · Time Series

Defu Cao, Wen Ye, Yizhou Zhang, Sam Griesemer, Yan Liu

Time series analysis underpins scientific advances. While specialized models have advanced various time series tasks, scientific domains face unique challenges: limited samples with complex physical dynamics, missing observations, multi-resolution sampling, and requirements for physical consistency. With the increasing demands on generative modeling capabilities, we introduce PINFDiT, a diffusion transformer-based model with physics injection during inference. Our approach combines a transformer backbone for capturing temporal dependencies with a comprehensive masking strategy that addresses imperfect data. The diffusion framework enables high-quality sample generation with inherent generative capability. In addition, our model-free physics-guided correction steers generated samples toward physically consistent solutions using calibrated Langevin dynamics, which balances distribution fidelity and physical law adherence without architectural modifications or retraining. Our evaluation demonstrates PINFDiT's effectiveness across multivariate forecasting with imperfect data, physics knowledge incorporation in data-limited scenarios, zero-shot and fine-tuning performance across diverse domains, establishing it as a proto-foundation model that bridges the gap between general-purpose and domain-specific models.

Deep Learning · Everything Else

Tianshi Zheng, Kiu Wai Tam, Kim Hue Nam Nguyen, Baixuan Xu, Zhaowei Wang, Cheng Jiayang, Hong Ting Tsang, Weiqi Wang, Jiaxin Bai, Tianqing Fang 等

Large language models (LLMs) are emerging as powerful tools for scientific law discovery, a foundational challenge in AI-driven science. However, existing benchmarks for this task suffer from a fundamental methodological trilemma, forcing a trade-off between scientific relevance, scalability, and resistance to memorization. Furthermore, they oversimplify discovery as static function fitting, failing to capture the authentic scientific process of uncovering embedded laws through the interactive exploration of complex model systems. To address these critical gaps, we introduce **NewtonBench**, a benchmark comprising 324 scientific law discovery tasks across 12 physics domains. Our design mitigates the evaluation trilemma by using counterfactual law shifts - systematic alterations of canonical laws - to generate a vast suite of problems that are scalable, scientifically relevant, and memorization-resistant. Moreover, we elevate the evaluation from static function fitting to interactive model discovery, requiring agents to experimentally probe simulated complex systems to uncover hidden principles. Our extensive evaluation of 11 state-of-the-art LLMs reveals a clear but fragile capability for discovery in frontier models: this ability degrades precipitously with increasing system complexity and exhibits extreme sensitivity to observational noise. Notably, we uncover a paradoxical effect of tool assistance: providing a code interpreter can hinder more capable models by inducing a premature shift from exploration to exploitation, causing them to satisfice on suboptimal solutions. These results demonstrate that robust, generalizable discovery in complex, interactive environments remains the core challenge for the future of automated science. By providing a scalable, robust, and scientifically authentic testbed, NewtonBench offers a crucial tool for measuring true progress and guiding the development of next-generation AI agents capable of genuine scientific discovery.

Deep Learning · Generative Models and Autoencoders

Robert Gruhlke, Valentin Resseguier, Merveille Talla

We introduce a new class of generative models based on multiplicative score-driven diffusion. In contrast to classical diffusion models that rely on additive Gaussian noise, our construction is driven by skew-symmetric multiplicative noise. It yields conservative forward-backward dynamics inspired by principles of physics. We prove that the forward process converges exponentially fast to a tractable non-Gaussian latent distribution, and we characterize this limit explicitly. A key property of our diffusion is that it preserves the distribution of data norms, resulting in a latent space that is inherently data-aware. Unlike the standard Gaussian prior, this structure better adapts to heavy-tailed and anisotropic data, providing a closer match between latent and observed distributions. On the algorithmic side, we derive the reverse-time stochastic differential equation and associated probability flow, and show that sliced score matching furnishes a consistent estimator for the backward dynamics. This estimation procedure is equivalent to maximizing an evidence lower bound (ELBO), bridging our framework with established variational principles. Empirically, we demonstrate the advantages of our model in challenging settings, including correlated Cauchy distributions and experimental fluid dynamics data (d=1024). Across these tasks, our approach more accurately captures extreme events and tail behavior than classical diffusion models, particularly in the low-data regime. Our results suggest that multiplicative conservative diffusions open a principled alternative to current score-based generative models, with strong potential for domains where rare but critical events dominate.

General Machine Learning · Representation Learning

Ya Wen, Jixuan Cai, Qiyao Ma, Linyan Li, Xinhuan Chen, Chris Webster, Yulun Zhou

Representation learning of geospatial locations remains a core challenge in achieving general geospatial intelligence, with increasingly diverging philosophies and techniques. While Earth observation paradigms excel at depicting locations in their physical states, we propose that a location’s full characterization requires grounding in both its physical attributes and its internal human activity pattern, the latter being particularly crucial for understanding its human-centric functions. We present MoRA, a human-centric geospatial framework that leverages a mobility graph as its core backbone to fuse various data modalities, aiming to learn embeddings that represent the socio-economic context and functional role of a location. MoRA achieves this through the integration of spatial tokenization, GNNs, and asymmetric contrastive learning to align 100M+ POIs, massive remote sensing imagery, and structured demographic statistics with a billion-edge mobility graph, ensuring the three auxiliary modalities are interpreted through the lens of fundamental human dynamics. To rigorously evaluate the effectiveness of MoRA, we construct a benchmark dataset composed of 9 downstream prediction tasks across social and economic domains. Experiments show that MoRA, with four input modalities and a compact 128-dimensional representation space, achieves superior predictive performances than state-of-the-art models by an average of 12.9\%. Echoing LLM scaling laws, we further demonstrate the scaling behavior in geospatial representation learning. We open-source code and pretrained models at: https://github.com/ylzhouchris/MoRA.

Applications · Physics

Jianing Huang, Kaixuan Zhang, Youjia Wu, Ze Cheng

Neural operators have become increasingly popular in solving partial differential equations (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the data-hungry nature of operator learning inevitably poses a bottleneck for their widespread applications. At the core of the challenge lies the absence of transferability of neural operators to new geometries. To tackle this issue, we propose operator learning with domain decomposition, a local-to-global framework to solve PDEs on arbitrary geometries. Under this framework, we devise an iterative scheme Schwarz Neural Inference (SNI). This scheme allows for partitioning of the problem domain into smaller subdomains, on which local problems can be solved with neural operators, and stitching local solutions to construct a global solution. Additionally, we provide a theoretical analysis of the convergence rate and error bound. We conduct extensive experiments on several representative linear and nonlinear PDEs with diverse boundary conditions and achieve remarkable geometry generalization compared to alternative methods.These analysis and experiments demonstrate the proposed framework's potential in addressing challenges related to geometry generalization and data efficiency. The code is publicly available at this repository: https://github.com/questionstorer/sni.