Scientific Simulation

Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Proper Orthogonal Decomposition (POD) coefficient space, exploiting the orthogonality of POD modes to impose an interpretable, variance-ordered latent geometry. This design enables efficient ensemble generation, preserves dominant spatial structure, and yields spatially interpretable, well-calibrated uncertainty at substantially lower computational cost. We evaluate PODiff on sea surface temperature downscaling over the West Australian coast and on a controlled advection--diffusion benchmark. PODiff achieves reconstruction accuracy comparable to pixel-space and learned-latent diffusion while using a substantially smaller structured latent space, requiring significantly less memory, and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.

Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy. While ideally suited for analog implementation, such hardware does not exist yet, and thus, in practice, PC is predominantly *digitally simulated*, requiring excessive amounts of compute while struggling to scale to deeper architectures. This paper reformulates PC to overcome this hardware-algorithm mismatch. First, we uncover how the canonical state-based formulation of PC (sPC) is, by design, deeply inefficient in digital simulation, inevitably resulting in exponential signal decay that stalls the entire numerical process. Then, to overcome this fundamental limitation, we introduce error-based PC (ePC), a novel reparameterization of PC which does not suffer from signal decay. Though no longer directly implementable in analog, ePC numerically computes *exact* PC weights gradients and runs orders of magnitude faster than sPC. Experiments across multiple architectures and datasets demonstrate that ePC matches backpropagation's performance even for deeper models where sPC struggles. Besides practical improvements, our work provides theoretical insight into PC dynamics and establishes a foundation for scaling PC-based learning to deeper architectures in digital simulation and beyond.

Generalized Bayesian Inference (GBI) tempers a loss with a temperature $\beta>0$ to mitigate overconfidence and improve robustness under model misspecification, but existing GBI methods typically rely on costly MCMC or SDE-based samplers and must be re-run for each new dataset and each $\beta$-value. We give the first fully amortized variational approximation for the specific case of the tempered posterior family $p_\beta(\theta\mid x) \propto \pi(\theta)p(x \mid\\theta)^\beta$ by training a single $(x,\beta)$-conditioned neural posterior estimator $q_\phi(\theta \mid x, \beta)$ that enables sampling in a single forward pass, without simulator calls or inference-time MCMC. We introduce two complementary training routes: (i) synthesizes off-manifold samples $(\theta, x) \sim \pi(\theta)p(x \mid \theta)^\beta$ and (ii) reweights a fixed base dataset $\pi(\theta)p(x \mid \theta)$ using self-normalized importance sampling (SNIS), where we show that the SNIS-weighted objective provides a consistent forward-KL fit to the tempered posterior with finite weight variance. Across four standard simulation-based inference (SBI) benchmarks—including the chaotic Lorenz–96 system—our $\beta$-amortized estimator achieves competitive posterior approximations, in standard two-sample metrics, with non-amortized MCMC-based power-posterior samplers over a wide range of temperatures.

Scientific embodied agents could automate laboratory workflows, but laboratory success is trajectory-level: an agent must remain safe throughout execution, not merely reach a final goal. In benchtop settings a small pose, force, or tilt error can cause irreversible spillage or equipment damage, yet most robot benchmarks evaluate reversible, high-tolerance manipulation and imitation-trained policies receive no recovery signal for execution drift. We introduce SafeLab, a generative simulation benchmark that couples a verified generative engine, an automated expert for teleoperation-free demonstrations, and a safety-aware RL interface, with 63 calibrated laboratory assets, 64 tasks across 9 manipulation categories, and 6,400 expert trajectories. Across state-of-the-art policies, it reveals unsafe-but-successful trajectories—large gaps between task success and Safe Success Rate—most acutely in liquid handling, force-limited actuation, and bimanual glassware rearrangement. Bounded residual RL then learns execution-level corrections that raise the simulated Safe Success Rate by up to 43.0 percentage points without retraining the base policy. Finally, 50 open-loop physical replays show 86% agreement between simulated and observed safety outcomes, supporting SafeLab as a scalable platform for screening and training safer laboratory agents.

Simulation-based inference (SBI) enables amortized Bayesian inference by first training a neural posterior estimator (NPE) on prior-simulator pairs, typically through low-dimensional summary statistics, which can then be cheaply reused for fast inference by querying it on new test observations. Because NPE is estimated under the training data distribution, it is susceptible to misspecification when observations deviate from the training distribution. Many robust SBI approaches address this by modifying NPE training or introducing error models, coupling robustness to the inference network and compromising amortization and modularity. We introduce minimum-distance summaries, a post-hoc robust NPE method that adapts queried test-time summaries independently of the pretrained NPE. Leveraging the maximum mean discrepancy (MMD) as a distance between observed data and a summary-conditional predictive distribution, the adapted summary displays strong robustness properties due to the robustness of the MMD. We demonstrate that the algorithm can be implemented efficiently with random Fourier feature approximations, yielding a lightweight, model-free test-time adaptation procedure. We provide theoretical guarantees for the robustness of our algorithm and empirically evaluate it on a range of synthetic and real-world tasks, demonstrating substantial robustness gains compared with existing robust SBI methods with minimal additional overhead.

LLM-based multi-agent simulations are increasingly adopted across application domains, but remain difficult to scale due to GPU memory pressure. Each agent maintains private GPU-resident states, including models, prefix caches, and adapters, which quickly exhaust device memory as the agent count grows. We identify two key properties of these workloads: sparse agent activation and an estimable agent invocation order. Based on an analysis of representative workload classes, we introduce invocation distance, a unified abstraction that estimates the relative order in which agents will issue future LLM requests. Leveraging this abstraction, we present ScaleSim, a memory-efficient LLM serving system for large-scale multi-agent simulations. ScaleSim enables proactive prefetching and priority-based eviction, supports diverse agent-specific memory through a modular interface, and achieves up to 1.74$\times$ speedup over SGLang on simulation benchmarks. ScaleSim's source code is available at https://github.com/PanZaifeng/KVFlow.

Large Language Models (LLMs) have shown significant potential in scientific discovery but struggle to bridge the gap between theoretical reasoning and verifiable physical simulation. Existing solutions operate in a passive "execute-then-response" loop and thus lack runtime perception, obscuring agents to transient anomalies (e.g., numerical instability or diverging oscillations). To address this limitation, we propose EmbodiedAct, a framework that transforms established scientific software into active embodied agents by grounding LLMs in embodied actions with a tight perception-execution loop. We instantiate EmbodiedAct within MATLAB and evaluate it on complex engineering design and scientific modeling tasks. Extensive experiments show that EmbodiedAct significantly outperforms existing baselines, achieving SOTA performance by ensuring satisfactory reliability and stability in long-horizon simulations and enhanced accuracy in scientific modeling.

The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis. While algebraic multigrid (AMG) offers optimal linear scaling, its performance is severely constrained by the trade-off between the sparsity and convergence quality of coarse-grid operators. Classical AMG heuristics struggle to balance these objectives, often sacrificing stability or performance for sparsity. We propose RAPNet, a graph neural network (GNN) framework that resolves this trade-off by learning to generate sparse, robust coarse operators directly from the sparse algebraic system. Key to our approach is a level-wise training strategy that enables learning from small subgraphs and generalization to million-node domains, bypassing the bottlenecks of prior neural AMG attempts. RAPNet executes exclusively during the solver setup phase, ensuring that the solve phase retains its favorable computational properties. We show that our method outperforms classical non-Galerkin baselines on diverse PDE discretizations and graph Laplacians, making it particularly effective for multi-query tasks such as eigenproblems, time-dependent simulations, and inverse or design problems.

Simulation plays a central role in scientific discovery. In many applications, the bottleneck is no longer running a simulator—it is choosing among large families of plausible simulators, each corresponding to different forward models/hypotheses consistent with observations. Over large model families, classical Bayesian workflows for model-selection are impractical. Furthermore, amortized model-selection methods typically hard-code a fixed model prior—or complexity penalty—at training time, requiring users to commit to a particular parsimony assumption before seeing the data. We introduce PRISM, a simulation-based encoder-decoder that infers a joint posterior over both discrete model structures and associated continuous parameters, while enabling test-time control of model complexity via a tunable model prior that the network is conditioned on. We show that PRISM scales to families with combinatorially many (up to billions of) model instantiations on a synthetic symbolic regression task. As a scientific application, we evaluate PRISM on biophysical modeling for diffusion MRI data, showing the ability to perform model selection across several multi-compartment models, on both synthetic and in-vivo neuroimaging data.

Neural simulators promise efficient surrogates for physics simulation, but scaling them is bottlenecked by the prohibitive cost of generating high-fidelity training data. Pre-training on abundant off-the-shelf geometries offers a natural alternative, yet faces a fundamental gap: supervision on static geometry alone ignores dynamics and can lead to negative transfer on physics tasks. We present GeoPT, a unified pre-trained model for general physics simulation based on lifted geometric pre-training. The core idea is to augment geometry with synthetic dynamics, enabling dynamics-aware self-supervision without physics labels. Pre-trained on over one million samples, GeoPT consistently improves industrial-fidelity benchmarks spanning fluid mechanics for cars, aircraft, and ships, and solid mechanics in crash simulation, reducing labeled data requirements by 20-60% and accelerating convergence by 2$\times$. These results show that lifting with synthetic dynamics bridges the geometry-physics gap, unlocking a scalable path for neural simulation and potentially beyond. Code is available at https://github.com/Physics-Scaling/GeoPT.

Reconstructing spatiotemporal fields from partial observations is fundamental to scientific inference, from inferring atmospheric states from satellite data to recovering fluid states from imaging. When observations are incomplete, the inverse problem is fundamentally ill-posed: even when the underlying PDE dynamics are Markovian in the full state, partial observation operators induce a non-Markovian posterior that cannot be resolved from a single timestep. We propose a history-bootstrapped autoregressive flow matching (HB-ARFM) for spatiotemporal inverse reconstruction under partial observability. Observation history bootstraps the initial reconstruction via conditional flow matching, resolving ambiguities. The same conditional transport model is then applied autoregressively, conditioning on both new observations and past predictions to propagate the reconstruction forward in time. We evaluate the method on boiling dynamics reconstruction, recovering full velocity and temperature fields from interface geometry and motion. Across two inverse tasks with varying observation sparsity, HB-ARFM produces physically and temporally valid reconstructions where other models fail.

We introduce Euler--Poincar\'e Neural Dynamics (EPND), a geometric-mechanics framework that casts evolution-operator learning as Lie-group flows for long-horizon dynamical modeling. Unlike conventional operator-learning approaches that treat temporal propagation as an unconstrained black-box map, EPND places geometric mechanics at the core of its architecture, playing a role of the mathematical engine. This foundation enables a principled treatment of curvature, symmetry, and conservation, with the learned evolution expressed in geometric terms. Building on this foundation, we develop the Euler--Poincar\'e Parallel Scan, a parallel algorithm that leverages the associative algebra of Lie-group compositions to overcome the inefficiencies of sequential computation. By unifying geometric structure with scalable computation, EPND achieves high accuracy, strong stability, and significant parallel acceleration in modeling long-horizon dynamics in versatile scientific simulations.

We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we introduce General-Geometry Neural Whitney Forms (Geo-NeWF): a data-driven finite element method. We jointly learn a differential operator and compatible reduced finite element spaces defined on the underlying geometry. The resulting model is solved to generate predictions, while exactly preserving physical conservation laws through Finite Element Exterior Calculus. Geometry enters the model as a discretized mesh both through a transformer-based encoding and as the basis for the learned finite element spaces. This explicitly connects the underlying geometry and imposed boundary conditions to the solution, providing a powerful inductive bias for learning neural PDEs which we demonstrate improves generalization to unseen domains. We provide a novel parameterization of the constitutive model ensuring existence and uniqueness of the solution. Our approach demonstrates state-of-the-art performance on several steady-state PDE benchmarks and provides a significant improvement over conventional baselines on out-of-distribution geometries.

Symbolic regression (SR) aims to discover interpretable analytical expressions that accurately describe observed data. Amortized SR promises to be much more efficient than the predominant genetic programming SR methods, but currently struggles to scale to realistic scientific complexity. We find that a key obstacle is the lack of a fast reduction of equivalent expressions to a concise normalized form. Amortized SR has addressed this with general-purpose Computer Algebra Systems (CAS) like SymPy, but the high computational cost severely limits training and inference speed. We propose **SimpliPy**, a rule-based simplification engine achieving a 100-fold speed-up over SymPy at comparable quality. This enables substantial improvements in amortized SR, including scalability to much larger training sets, more efficient use of the per-expression token budget, and systematic training set decontamination with respect to equivalent test expressions. We demonstrate these advantages in our **Flash-ANSR** framework, which achieves much better accuracy than amortized baselines (NeSymReS, E2E) on the FastSRB benchmark. Moreover, it performs on par with state-of-the-art direct optimization (PySR) while recovering more concise rather than more complex expressions with increasing inference budget.

Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying physics. In many PDE regimes, the induced global interaction kernels are empirically compressible, exhibiting rapid spectral decay that admits low-rank approximations. We leverage this observation to unify representative global mixing modules in neural operators under a shared low-rank template: compressing high-dimensional pointwise features into a compact latent space, processing global interactions within it, and reconstructing the global context back to spatial points. Guided by this view, we introduce Low-Rank Spatial Attention (LRSA) as a clean and direct instantiation of this template. Crucially, unlike prior approaches that often rely on non-standard aggregation or normalization modules, LRSA is built purely from standard Transformer primitives, i.e., attention, normalization, and feed-forward networks, yielding a concise block that is straightforward to implement and directly compatible with hardware-optimized kernels. In our experiments, such a simple construction is sufficient to achieve high accuracy, yielding an average error reduction of over 17\% relative to second-best methods, while remaining stable and efficient in mixed-precision training.

Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data. A persistent challenge, however, is model misspecification. In a Bayesian setting, targeting posterior distributions, errors may arise from the simulator, the noise or prior modelling. These model components are only approximations of reality, and severe mismatches can yield biased or overconfident posteriors. We address this issue by introducing Flow Matching Corrected Posterior Estimation (FMCPE), a framework that leverages the flow matching paradigm to refine simulation-trained posterior estimators using a small set of calibration samples. Our approach proceeds in two stages: first, a posterior approximator is trained on abundant simulated data; second, flow matching transports its predictions toward the true posterior supported by calibration observations. We rely on the later to guide the correction, without requiring explicit knowledge of the misspecification form or of which model components are affected. This design enables FMCPE to combine the scalability of SBI with robustness to distributional shift. Across synthetic benchmarks and real-world datasets, we show that our proposal consistently mitigates the effects of misspecification, delivering improved inference accuracy and uncertainty quantification compared to standard SBI baselines, while remaining computationally efficient.

Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis. Existing unbalanced Optimal Transport (OT) methods treat mass as a continuous fluid, performing inference at the population level. However, this macroscopic view often fails to capture the discrete, jump-like nature of birth-death events at single-cell resolution, which is essential for understanding lineage branching and fate decisions. We present **Unbalanced Schrödinger Bridge (USB)**, a simulation-free framework for learning underlying dynamics that effectively integrates both stochastic and unbalanced effects which also models the discrete, jump-like birth–death dynamics at single-cell resolution. Theoretically, USB provides a tractable solution to the Branching Schrödinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps. Technically, the method implements an efficient solver by introducing a simulation-free training objective that effectively scales to high-dimensional omics data. Empirically, we demonstrate on both simulated and real-world datasets that USB not only achieves trajectory reconstruction performance better than or comparable to deterministic baselines but also uniquely enables realistic discrete simulation of birth-death dynamics at single-cell resolution.

Conventional patchified Transformers operate on uniform spatial partitions, distributing computational effort evenly across the domain irrespective of local features. This inflexible tokenization scheme is inherently limited in its ability to efficiently represent and process solutions to complex PDEs. To address this, we propose MeshTok, an adaptive mesh refinement (AMR)-inspired tokenization and sequence modeling framework. This method selectively refines spatial regions exhibiting sharp gradients, transient features, or multiscale structures, generating a heterogeneous set of multiscale tokens defined on a fixed simulation grid. These tokens are processed within a unified Transformer sequence, enabling the model to simultaneously capture coarse-grained global context and fine-grained local details without requiring specialized architectural components. Although adaptive refinement moderately increases token count, it promotes a more targeted allocation of computational resources to physically informative regions, which we view as a practical inductive bias rather than a formal optimality guarantee. Experimental evaluations across multiple PDE families and benchmark datasets demonstrate that MeshTok consistently improves the efficiency-accuracy trade-off compared to uniform-grid baselines. This suggests adaptive multiscale tokenization as a scalable and generalizable design principle for neural PDE modeling. Code is available at https://github.com/SCAILab-USTC/MeshTok.

The two-sample testing problem, a fundamental task in statistics and machine learning, seeks to determine whether two sets of samples, drawn from underlying distributions $p$ and $q$, are in fact identically distributed (i.e.~whether $p=q$). A popular and intuitive approach is the classifier two-sample test (C2ST), where a classifier is trained to distinguish between samples from $p$ and $q$. Yet despite simplicity of the C2ST, its reliability hinges on access to a near-Bayes-optimal classifier, a requirement that is rarely met and difficult to verify. This raises a major open question: can a weak classifier still be useful for two-sample testing? We show that the answer is a definitive yes. Building on the work of Hu & Lei (2024), we analyze two conformal variants of the C2ST that convert the scores from any trained classifier---even if weak, biased, or overfit---into exact, finite-sample p-values. We establish two key theoretical properties of the conformal C2ST: (i) finite-sample Type-I error control, and (ii) non-trivial power that degrades gently in tandem with the error of the trained classifier. The upshot is that even poorly performing classifiers can yield powerful and reliable two-sample tests. This general framework finds a powerful application in Bayesian inference, particularly for validating Neural Posterior Estimation (NPE) models, where the task of comparing a learned posterior approximation $q(\theta \mid y)$ to the true posterior $p(\theta \mid y)$ can be framed as a two-sample test. Empirically, the Conformal C2ST outperforms classical discriminative tests across a wide range of benchmarks for this task. Our results establish the conformal C2ST as a practical, theoretically grounded diagnostic tool.

The ability to use tools is fundamental for large language model (LLM) agents. Given a task, existing systems use LLMs to plan and generate tool calls, which are executed by real-world tools to complete the task. However, tool calls are prone to errors because they are generated primarily from the intrinsic capabilities of LLMs. Moreover, while it is useful to let LLMs iteratively refine the tool-call sequence using execution results from real tools, this process can be expensive and may cause unsafe side effects. To improve LLM tool calls and address issues caused by using real tools for refinement, we introduce Gecko, a stateful simulation environment that provides informative feedback for refining LLM tool calls before real execution. Specifically, Gecko combines rules and LLMs to check the validity of tool names and arguments, synthesize schema-conforming and state-consistent responses, and judge task completion against the user objective. These three types of feedback allow LLMs to refine their tool calls in simulation, forming a simple yet effective test-time scaling method named GATS. On BFCLv3 and $\tau^2$-bench, GATS consistently improves the performance of various LLMs, including GPT-4o, GPT-5, and Gemini-3.0-pro.