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Ling Guo

Publications and source records attributed to Ling Guo.

At least 19 recordsLinked to original sources
arXiv2026

Deep operator learning for efficient sampling from invariant measures of stochastic differential equations

We introduce an amortized neural sampler that combines operator learning with flow methods for sampling. It maps SDE coefficient functions to pushforwards from a reference measure to the invariant measures, enabling efficient sampling across families of stochastic differential equations. Our framework shifts traditional sampling cost to an initial training phase, after which new SDE instances require only one encoder pass and a few ODE solver steps, independent of mixing time. To handle problems in high dimensions, we use Lagrangian trajectory sensors for the coefficient functions and cross attention in the architecture. We also theoretically establish the expressivity and resolution invariance of our framework. Experiments on 1D and 2D SDE families show competitive accuracy with substantial speedups over MCMC in regimes with slow mixing, transfer across sensor counts, and demonstration results on a 64D interacting particle SDE where traditional grid approaches are infeasible.

math.NA↗
arXiv2026

Chain of Operators: An Inference-Time Harness for In-Context Operator Learning

While scientific foundation models show immense promise in accelerating physical simulations and numerical forecasting, they remain notoriously brittle when encountering out-of-distribution (OOD) scenarios. Adapting these generalist models to complex OOD tasks typically requires expensive parameter fine-tuning. In linguistic AI, this bottleneck is bypassed using "harnesses", which serve as external scaffolding such as reasoning chains and tool use to adapt frozen weights to complex tasks, yet designing an equivalent harness for physical domains remains an open frontier. To bridge this gap, we introduce Chain of Operators (CHOP), a framework that guides a frozen foundation model through complex OOD tasks without updating a single weight. By exploiting the in-context learning capability of In-Context Operator Networks (ICON), CHOP systematically decomposes unfamiliar problems into a sequence of explicit, closed-form mathematical operations and multiple model calls, translating OOD queries back into the model's learned operating regime. Across diverse benchmarks, including canonical PDE problems and real-world air-quality forecasting, CHOP consistently and substantially reduces inference errors compared to direct model evaluation. Crucially, these modular operator chains remain fully interpretable and can generalize across entirely distinct families of physical equations. Ultimately, this work demonstrates how frozen scientific models can adapt through programmable inference, establishing a modular, potential paradigm for agentic scientific computing.

cs.LG↗
arXiv2026

Flow-based generative models for amortized Bayesian inference in regression and inverse PDE problems

Bayesian inference provides a principled framework for uncertainty quantification in scientific machine learning. However, conventional Bayesian approaches usually require solving a new inference problem for each observation set, causing substantial computational costs that hinder real-time applications like online monitoring and digital twins. Furthermore, inferring over infinite-dimensional function spaces with varying observation sets poses major challenges for existing amortized inference methods. In this work, we propose Flow-ABI, a flow-based generative framework for amortized Bayesian inference in regression and inverse partial differential equation (PDE) problems. It consists of two components: (i) a functional prior model that learns expressive priors from historical data and physical knowledge through flow matching, and (ii) a set-conditioned functional posterior sampler mapping observation sets to functional posterior distributions. The learned posterior model naturally accommodates varying, permutation-invariant observation sets, and generalizes across different observation discretizations. Once trained, Flow-ABI enables near-real-time posterior sampling for previously unseen observations without retraining or iterative optimization. The proposed methodology can be seamlessly integrated with a wide class of scientific machine learning frameworks, including physics-informed neural networks and neural operators, for uncertainty-aware inverse PDE modeling. Experiments demonstrate that Flow-ABI accurately captures both Gaussian and non-Gaussian posterior distributions while achieving over two-order-of-magnitude speedups relative to the gold-standard Bayesian inference method, Hamiltonian Monte Carlo. These results show Flow-ABI is an effective, scalable, and computationally efficient framework for uncertainty quantification in scientific machine learning.

physics.comp-ph↗
arXiv2026

Physics-guided correction for operator learning under model misspecification

Physics-informed operator learning provides an efficient framework for approximating solution operators of partial differential equations by combining observational data with governing physical laws. However, most existing methods implicitly assume that the prescribed governing equation is accurate. This assumption may fail in practical applications, where model simplifications, missing physical effects, parameter drift, or incomplete constitutive relations can lead to model misspecification. In this work, we propose a physics-guided operator correction framework for learning solution operators under misspecified governing equations. At the operator level, the target mapping is decomposed into a prior operator induced by an approximate physical model and a learnable correction operator that accounts for the remaining discrepancy. We realize the operator model correction using a serial DeepONet architecture, where the first DeepONet provides a solution prediction and the second DeepONet learns an additive correction conditioned on both the input function and the solution prediction. The learned correction is incorporated into the physics residual and trained together with data-consistency constraints, allowing the model to retain useful physical structure while adapting to inaccurate governing equations. Numerical experiments on diffusion-reaction, Burgers, cavity flow, and hyperelastic problems show that the proposed method substantially reduces errors induced by misspecified physics. Additional tests under sparse and noisy observations further demonstrate the robustness of the framework and its ability to provide informative uncertainty estimates through deep ensembles.

math.NA↗
arXiv2026

Latent representation learning based model correction and uncertainty quantification for PDEs

Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning literature, existing correction methods typically operate in parameter space, where uncertainty is often quantified via sampling or ensemble-based methods, which can be prohibitive and motivates more efficient representation-level alternatives. To this end, we develop a latent-space model-correction framework by extending our previously proposed LVM-GP solver, which couples latent-variable model with Gaussian processes (GPs) for uncertainty-aware PDE learning. Our architecture employs a shared confidence-aware encoder and two probabilistic decoders, with the solution decoder predicting the solution distribution and the correction decoder inferring a discrepancy term to compensate for model-form errors. The encoder constructs a stochastic latent representation by balancing deterministic features with a GP prior through a learnable confidence function. Conditioned on this shared latent representation, the two decoders jointly quantify uncertainty in both the solution and the correction under soft physics constraints with noisy data. An auxiliary latent-space regularization is introduced to control the learned representation and enhance robustness. This design enables joint uncertainty quantification of both the solution and the correction within a single training procedure, without parameter sampling or repeated retraining. Numerical experiments show accuracy comparable to Ensemble PINNs and B-PINNs, with improved computational efficiency and robustness to misspecified physics.

math.NA↗
arXiv2026

ViHOI: Human-Object Interaction Synthesis with Visual Priors

Generating realistic and physically plausible 3D Human-Object Interactions (HOI) remains a key challenge in motion generation. One primary reason is that describing these physical constraints with words alone is difficult. To address this limitation, we propose a new paradigm: extracting rich interaction priors from easily accessible 2D images. Specifically, we introduce ViHOI, a novel framework that enables diffusion-based generative models to leverage rich, task-specific priors from 2D images to enhance generation quality. We utilize a large Vision-Language Model (VLM) as a powerful prior-extraction engine and adopt a layer-decoupled strategy to obtain visual and textual priors. Concurrently, we design a Q-Former-based adapter that compresses the VLM's high-dimensional features into compact prior tokens, which significantly facilitates the conditional training of our diffusion model. Our framework is trained on motion-rendered images from the dataset to ensure strict semantic alignment between visual inputs and motion sequences. During inference, it leverages reference images synthesized by a text-to-image generation model to improve generalization to unseen objects and interaction categories. Experimental results demonstrate that ViHOI achieves state-of-the-art performance, outperforming existing methods across multiple benchmarks and demonstrating superior generalization.

cs.CV↗
arXiv2026

FNWoS: Fractional Neural Walk-on-Spheres Methods for High-Dimensional PDEs Driven by $\alpha$-stable L\'{e}vy Process on Irregular Domains

In this paper, we develop a highly parallel and derivative-free fractional neural walk-on-spheres method (FNWoS) for solving high-dimensional fractional Poisson equations on irregular domains. We first propose a simplified fractional walk-on-spheres (FWoS) scheme that replaces the high-dimensional normalized weight integral with a constant weight and adopts a correspondingly simpler sampling density, substantially reducing per-trajectory cost. To mitigate the slow convergence of standard Monte Carlo sampling, FNWoS is then proposed via integrating this simplified FWoS estimator, derived from the Feynman-Kac representation, with a neural network surrogate. By amortizing sampling effort over the entire domain during training, FNWoS achieves more accurate evaluation at arbitrary query points with dramatically fewer trajectories than classical FWoS. To further enhance efficiency in regimes where the fractional order $\alpha$ is close to 2 and trajectories become excessively long, we introduce a truncated path strategy with a prescribed maximum step count. Building on this, we propose a buffered supervision mechanism that caches training pairs and progressively refines their Monte Carlo targets during training, removing the need to precompute a highly accurate training set and yielding the buffered fractional neural walk-on-spheres method (BFNWoS). Extensive numerical experiments, including tests on irregular domains and problems with dimensions up to $1000$, demonstrate the accuracy, scalability, and computational efficiency of the proposed methods.

math.NA↗
arXiv2026

Reconstruction-Anchored Diffusion Model for Text-to-Motion Generation

Diffusion models have seen widespread adoption for text-driven human motion generation and related tasks due to their impressive generative capabilities and flexibility. However, current motion diffusion models face two major limitations: a representational gap caused by pre-trained text encoders that lack motion-specific information, and error propagation during the iterative denoising process. This paper introduces Reconstruction-Anchored Diffusion Model (RAM) to address these challenges. First, RAM leverages a motion latent space as intermediate supervision for text-to-motion generation. To this end, RAM co-trains a motion reconstruction branch with two key objective functions: self-regularization to enhance the discrimination of the motion space and motion-centric latent alignment to enable accurate mapping from text to the motion latent space. Second, we propose Reconstructive Error Guidance (REG), a testing-stage guidance mechanism that exploits the motion diffusion model's inherent self-correction ability to mitigate error propagation. At each denoising step, REG uses the motion reconstruction branch to reconstruct the previous estimate, reproducing the prior error patterns. By amplifying the residual between the current prediction and the reconstructed estimate, REG highlights the improvements in the current prediction. Extensive experiments demonstrate that RAM achieves significant improvements and state-of-the-art performance. Our code will be released.

cs.CV↗
arXiv2025

Deep set based operator learning with uncertainty quantification

Learning operators from data is central to scientific machine learning. While DeepONets are widely used for their ability to handle complex domains, they require fixed sensor numbers and locations, lack mechanisms for uncertainty quantification, and are thus limited in practical applicability. Recent permutation-invariant extensions, such as the Variable-Input Deep Operator Network, relax these sensor constraints but still rely on sufficiently dense observations and cannot capture uncertainties arising from incomplete measurements or from operators with inherent randomness. To address these challenges, we propose UQ-SONet, a permutation-invariant operator learning framework with built-in uncertainty quantification. Our model integrates a set transformer embedding to handle sparse and variable sensor locations, and employs a conditional variational autoencoder to approximate the conditional distribution of the solution operator. By minimizing the negative ELBO, UQ-SONet provides principled uncertainty estimation while maintaining predictive accuracy. Numerical experiments on deterministic and stochastic PDEs, including the Navier-Stokes equation, demonstrate the robustness and effectiveness of the proposed framework.

cs.LG↗
arXiv2025

An RBC-MsUQ Framework for Red Blood Cell Morpho-Mechanics

Characterizing the morpho-mechanical properties of red blood cells (RBCs) is crucial for understanding microvascular transport mechanisms and cellular pathophysiological processes, yet current computational models are constrained by multi-source uncertainties including cross-platform experimental discrepancies and parameter identification stochasticity. We present RBC-MsUQ, a novel multi-stage uncertainty quantification framework tailored for RBCs. It integrates hierarchical Bayesian inference with diverse experimental datasets, establishing prior distributions for RBC parameters via microscopic simulations and literature-derived data. A dynamic annealing technique defines stress-free baselines, while deep neural network surrogates, optimized through sensitivity analysis, achieve sub-10$^{-2}$ prediction errors for efficient simulation approximation. Its two-stage hierarchical inference architecture constrains geometric and shear modulus parameters using stress-free state and stretching data in Stage I and enables full-parameter identification via membrane fluctuation and relaxation tests in Stage II. Applied to healthy and malaria-infected RBCs, the RBC-MsUQ framework produces statistically robust posterior distributions, revealing increased stiffness and viscosity in pathological cells. Quantitative model-experiment validation demonstrates that RBC-MsUQ effectively mitigates uncertainties through cross-platform data fusion, overcoming the critical limitations of existing computational approaches. The RBC-MsUQ framework thus provides a systematic paradigm for studying RBC properties and advancing cellular mechanics and biomedical engineering.

physics.bio-ph↗
arXiv2025

LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process

We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the input to a high-dimensional latent representation, enabling uncertainty-aware prediction of the solution. Specifically, the architecture consists of a confidence-aware encoder and a probabilistic decoder. The encoder implements a high-dimensional latent variable model based on a Gaussian process (LVM-GP), where the latent representation is constructed by interpolating between a learnable deterministic feature and a Gaussian process prior, with the interpolation strength adaptively controlled by a confidence function learned from data. The decoder defines a conditional Gaussian distribution over the solution field, where the mean is predicted by a neural operator applied to the latent representation, allowing the model to learn flexible function-to-function mapping. Moreover, physical laws are enforced as soft constraints in the loss function to ensure consistency with the underlying PDE structure. Compared to existing approaches such as Bayesian physics-informed neural networks (B-PINNs) and deep ensembles, the proposed framework can efficiently capture functional dependencies via merging a latent Gaussian process and neural operator, resulting in competitive predictive accuracy and robust uncertainty quantification. Numerical experiments demonstrate the effectiveness and reliability of the method.

stat.ML↗
arXiv2025

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems

Multi-scale PDE problems present significant challenges in scientific computing. While conventional MLP-based deep learning methods exhibit spectral bias in resolving multi-scale features, the physics-informed Kolmogorov-Arnold network (PIKAN) mitigates this issue through its novel architecture, demonstrating certain advantages. On the other hand, insights from the information bottleneck theory suggest that high-resolution training points are essential for these hybrid methods to accurately capture multi-scale behavior, although this requirement often leads to longer training times. To address this challenge, we propose a simple yet effective multi-resolution training-enhanced PIKAN framework, termed MR-PIKAN, which trains the data-physics hybrid model either sequentially or alternately across different resolutions. The proposed MR-PIKAN is validated on various multi-scale forward and inverse PDE problems. Numerical results indicate that this new training strategy effectively reduces computational costs without sacrificing accuracy, thereby enabling efficient solutions of complex multi-scale PDEs in both forward and inverse settings.

physics.comp-ph↗
arXiv2025

Addressing an extreme positivity violation to distinguish the causal effects of surgery and anesthesia via separable effects

The U.S. Food and Drug Administration has cautioned that prenatal exposure to anesthetic drugs during the third trimester may have neurotoxic effects; however, there is limited clinical evidence available to substantiate this recommendation. One major scientific question of interest is whether such neurotoxic effects might be due to surgery, anesthesia, or both. Isolating the effects of these two exposures is challenging because they are observationally equivalent, thereby inducing an extreme positivity violation. To address this, we adopt the separable effects framework of Robins and Richardson (2010) to identify the effect of anesthesia (alone) by blocking effects through variables that are assumed to completely mediate the causal pathway from surgery to the outcome. We apply this approach to data from the nationwide Medicaid Analytic eXtract (MAX) from 1999 through 2013, which linked 16,778,281 deliveries to mothers enrolled in Medicaid during pregnancy. Furthermore, we assess the sensitivity of our results to violations of our key identification assumptions.

stat.AP↗
arXiv2025

Guiding Human-Object Interactions with Rich Geometry and Relations

Human-object interaction (HOI) synthesis is crucial for creating immersive and realistic experiences for applications such as virtual reality. Existing methods often rely on simplified object representations, such as the object's centroid or the nearest point to a human, to achieve physically plausible motions. However, these approaches may overlook geometric complexity, resulting in suboptimal interaction fidelity. To address this limitation, we introduce ROG, a novel diffusion-based framework that models the spatiotemporal relationships inherent in HOIs with rich geometric detail. For efficient object representation, we select boundary-focused and fine-detail key points from the object mesh, ensuring a comprehensive depiction of the object's geometry. This representation is used to construct an interactive distance field (IDF), capturing the robust HOI dynamics. Furthermore, we develop a diffusion-based relation model that integrates spatial and temporal attention mechanisms, enabling a better understanding of intricate HOI relationships. This relation model refines the generated motion's IDF, guiding the motion generation process to produce relation-aware and semantically aligned movements. Experimental evaluations demonstrate that ROG significantly outperforms state-of-the-art methods in the realism and semantic accuracy of synthesized HOIs.

cs.CV↗
arXiv2025

Scalable physics-informed deep generative model for solving forward and inverse stochastic differential equations

Physics-informed deep learning approaches have been developed to solve forward and inverse stochastic differential equation (SDE) problems with high-dimensional stochastic space. However, the existing deep learning models have difficulties solving SDEs with high-dimensional spatial space. In the present study, we propose a scalable physics-informed deep generative model (sPI-GeM), which is capable of solving SDE problems with both high-dimensional stochastic and spatial space. The sPI-GeM consists of two deep learning models, i.e., (1) physics-informed basis networks (PI-BasisNet), which are used to learn the basis functions as well as the coefficients given data on a certain stochastic process or random field, and (2) physics-informed deep generative model (PI-GeM), which learns the distribution over the coefficients obtained from the PI-BasisNet. The new samples for the learned stochastic process can then be obtained using the inner product between the output of the generator and the basis functions from the trained PI-BasisNet. The sPI-GeM addresses the scalability in the spatial space in a similar way as in the widely used dimensionality reduction technique, i.e., principal component analysis (PCA). A series of numerical experiments, including approximation of Gaussian and non-Gaussian stochastic processes, forward and inverse SDE problems, are performed to demonstrate the accuracy of the proposed model. Furthermore, we also show the scalability of the sPI-GeM in both the stochastic and spatial space using an example of a forward SDE problem with 38- and 20-dimension stochastic and spatial space, respectively.

physics.comp-ph↗
arXiv2025

Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems

Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems is a fundamental yet challenging problem in many fields of science and engineering. Existing methods face significant obstacles: Gaussian-based filters struggle with non-Gaussian distributions, while sequential Monte Carlo methods are computationally intensive and prone to particle degeneracy in high dimensions. Although generative models in machine learning have made significant progress in modeling high-dimensional non-Gaussian distributions, their inefficiency in online updating limits their applicability to filtering problems. To address these challenges, we propose a flow-based Bayesian filter (FBF) that integrates normalizing flows to construct a novel latent linear state-space model with Gaussian filtering distributions. This framework facilitates efficient density estimation and sampling using invertible transformations provided by normalizing flows, and it enables the construction of filters in a data-driven manner, without requiring prior knowledge of system dynamics or observation models. Numerical experiments demonstrate the superior accuracy and efficiency of FBF.

math.NA↗
arXiv2024

Optimal Low-dimensional Approximation of Transfer Operators via Flow Matching: Computation and Error Analysis

Reaction coordinates (RCs) are low-dimensional representations of complex dynamical systems that capture their long-term dynamics. In this work, we focus on the criteria of lumpability and decomposability, previously established for assessing RCs, and propose a new flow matching approach for the analysis and optimization of reaction coordinates based on these criteria. This method effectively utilizes data to quantitatively determine whether a given RC satisfies these criteria and enables end-to-end optimization of the reaction coordinate mapping model. Furthermore, we provide a theoretical analysis of the relationship between the loss function used in our approach and the operator error induced by dimension reduction.

math.NA↗
arXiv2024

Energy based diffusion generator for efficient sampling of Boltzmann distributions

Sampling from Boltzmann distributions, particularly those tied to high dimensional and complex energy functions, poses a significant challenge in many fields. In this work, we present the Energy-Based Diffusion Generator (EDG), a novel approach that integrates ideas from variational autoencoders and diffusion models. EDG uses a decoder to generate Boltzmann-distributed samples from simple latent variables, and a diffusion-based encoder to estimate the Kullback-Leibler divergence to the target distribution. Notably, EDG is simulation-free, eliminating the need to solve ordinary or stochastic differential equations during training. Furthermore, by removing constraints such as bijectivity in the decoder, EDG allows for flexible network design. Through empirical evaluation, we demonstrate the superior performance of EDG across a variety of sampling tasks with complex target distributions, outperforming existing methods.

cs.LG↗