arXiv subjects

Shikai Fang

Publications and source records attributed to Shikai Fang.

At least 19 recordsLinked to original sources

arXiv2026

HarmoCore: Functional Latent Diffusion for Sparse Reconstruction of Oscillatory Wave Fields

Reconstructing oscillatory wave fields from scattered sensors is a severely underdetermined inverse problem. Beyond the challenges of general physical-field reconstruction, wave responses are complex-valued, frequency-sensitive, and highly oscillatory, while costly simulation and sensing often leave only extreme-sparse observations. Existing low-rank, operator, and diffusion approaches are largely designed for real-valued, smoother fields; dense pixel-space diffusion is particularly inefficient for oscillatory complex fields and difficult to scale to 3D. We propose HarmoCore, which places a generative prior in a compact, continuous, and structured wave-field latent. HarmoCore represents joint real--imaginary channels with Functional Tucker cores over shared continuous spatial bases, learns a frequency-conditioned core diffusion prior, and performs Diffusion Posterior Sampling directly in core space. At fixed sensor coordinates, the multilinear decoder induces an explicit likelihood guidance operator, avoiding dense pixel-space correction. Optional target-equation residual guidance further promotes physical consistency. Experiments on 2D Helmholtz, 2D synthetic wave fields, and 3D Helmholtz show substantial gains under 1%--2% sensing while remaining practical in three dimensions.

cs.LG↗

arXiv2026

TRACE: Retrospective Streaming Generation of Physical Fields under Sparse Structured Sensing

Reconstructing continuous physical fields from sparse measurements is central to scientific monitoring, inverse modeling, and digital-twin construction. Generative reconstruction has recently emerged as a promising paradigm for this task by learning data-driven physical priors that complete plausible full fields from limited observations. However, existing methods largely assume fixed, batch conditioning, whereas real sensing systems often produce structured streams: probes scan local regions, instruments observe moving fields of view, and communication constraints may leave entire frames missing. We propose TRACE, a retrospective streaming generative reconstruction framework for physical fields under structured sensing. TRACE performs approximate Bayesian inference in a learned continuous-coordinate latent space, converting sparse off-grid measurements into generative latent evidence, fusing it with a state-space temporal prior through Kalman-style filtering, and refining under-observed past frames via retrospective smoothing. Experiments on active matter, ocean sound-speed fields, and supernova simulations show that TRACE matches or surpasses frame-wise generative reconstructors, offline spatiotemporal methods, and streaming data-assimilation baselines in reconstruction quality under temporally sparse and spatially localized sensing protocols.

stat.ML↗

arXiv2026

Mitigating Spectral Bias in Neural Operators for Underwater Transmission Loss Prediction

Predicting underwater acoustic transmission loss rapidly and accurately is crucial for real-time ocean acoustic applications. While Fourier Neural Operators (FNO) have emerged as powerful surrogate models due to their global receptive fields, they suffer from spectral bias. The frequency truncation mechanism in FNO filters out high-frequency components, resulting in over-smoothed predictions that fail to capture fine-grained interference patterns. To overcome this limitation, this paper proposes a Spectral-Spatial Residual Learning (S2RL) framework. S2RL decomposes the prediction task into a coarse-to-fine process: a spectral Global Propagator first generates a globally consistent prediction, and a spatial Local Refiner subsequently recovers the high-frequency residuals. Experimental results on a South China Sea dataset show that the proposed method significantly outperforms FNO baselines while maintaining millisecond-level inference speeds.

cs.SD↗

arXiv2026

Battery-Sim-Agent: Leveraging LLM-Agent for Inverse Battery Parameter Estimation

Parameterizing high-fidelity "digital twins" of batteries is a critical yet challenging inverse problem that hinders the pace of battery innovation. Prevailing methods formulate this as a black-box optimization (BBO) task, employing algorithms that are sample-inefficient and blind to the underlying physics. In this work, we introduce a new paradigm that reframes the inverse problem as a reasoning task, and present Battery-Sim-Agent, the first framework to deploy a Large Language Model (LLM) agent in a closed loop with a high-fidelity battery simulator. The agent mimics a human scientist's workflow: it interprets rich, multi-modal feedback from the simulator, forms physically-grounded hypotheses to explain discrepancies, and proposes structured parameter updates. On a systematically constructed benchmark suite spanning diverse battery chemistries, operating conditions, and difficulty levels, our agent significantly outperforms strong BBO baselines like Bayesian optimization in identifying accurate parameters. We further demonstrate the framework's capability in complex long-horizon degradation fitting tasks and validate its practical applicability on real-world battery datasets. Our results highlight the promise of LLM-agents as reasoning-based optimizers for scientific discovery and battery parameter estimation.

cs.AI↗

arXiv2026

APEX: Amplitude Anchors and Phase Priors for Target-Scarce Higher-Frequency Wave Prediction

Learning-based surrogates have become increasingly effective for wave-field prediction, and neural operators in particular have shown strong performance within observed frequency regimes. However, higher-frequency prediction under scarce target supervision remains comparatively underexplored, especially in wave problems where higher-frequency data are substantially more expensive to simulate or measure than lower-frequency data. A central difficulty is that cross-frequency transfer is inherently asymmetric: coarse amplitude structure remains relatively stable across frequencies, whereas phase-sensitive oscillatory structure deteriorates much more rapidly as frequency increases. Motivated by this asymmetry, we propose APEX, Amplitude-anchored and Phase-prior-guided Enhancement from eXtrapolated coarse predictions, a framework for target-scarce higher-frequency wave-field prediction. A lower-frequency neural operator first provides a coarse prediction in the target-frequency regime, from which we retain only the amplitude as a transferable structural anchor. A conditional flow-matching enhancer then reconstructs the target higher-frequency field under the guidance of a Green's-function-inspired phase prior. Experiments on SimpleWave, Helmholtz, and Maxwell benchmarks show that APEX consistently outperforms direct lower-to-higher extrapolation, target-adapted operator, and joint generative baselines under limited target-frequency supervision. Our results suggest that reliable higher-frequency prediction of oscillatory wave fields should not rely on direct end-to-end transfer of the full complex field, but instead on explicitly reusing transferable coarse structure while separately recovering the missing oscillatory detail.

cs.LG↗

arXiv2026

StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Models

Inferring the evolution of high-dimensional and multi-modal (e.g., spatio-temporal) physical fields from irregular sparse measurements in real time is a fundamental challenge in science and engineering. Existing approaches, including diffusion-based generative models and functional tensor methods, typically operate in offline settings, depend on full temporal observations, or incur substantial inference cost. We propose StreamPhy, an end-to-end framework that enables efficient and accurate streaming inference of full-field physical dynamics from incoming irregular sparse measurements. The framework integrates a data-adaptive observation encoder that is robust to arbitrary observation patterns, a structured state-space model that supports memory-efficient online updates across irregular time intervals, and an expressive Functional Tensor Feature-wise Linear Modulation (FT-FiLM) decoder for continuous-field generation. We prove that FT-FiLM is more expressive than the functional Tucker model, admitting a richer function class for handling complex dynamics. Experiments on three representative physical systems under challenging sampling patterns show that StreamPhy consistently outperforms state-of-the-art baselines, with at least 48\% improvement in accuracy and up to 20--100X faster inference than diffusion-based methods.

cs.LG↗

arXiv2026

Reasoning as Gradient: Scaling MLE Agents Beyond Tree Search

LLM-based agents for machine learning engineering (MLE) predominantly rely on tree search, a form of gradient-free optimization that uses scalar validation scores to rank candidates. As LLM reasoning capabilities improve, exhaustive enumeration becomes increasingly inefficient compared to directed updates, analogous to how accurate gradients enable efficient descent over random search. We introduce Gome, an MLE agent that operationalizes gradient-based optimization. Gome maps structured diagnostic reasoning to gradient computation, success memory to momentum, and multi-trace execution to distributed optimization. Under a closed-world protocol that isolates architectural effects from external knowledge, Gome achieves a state-of-the-art 35.1\% any-medal rate on MLE-Bench with a restricted 12-hour budget on a single V100 GPU. Scaling experiments across 10 models reveal a critical crossover: with weaker models, tree search retains advantages by compensating for unreliable reasoning through exhaustive exploration; as reasoning capability strengthens, gradient-based optimization progressively outperforms, with the gap widening at frontier-tier models. Given the rapid advancement of reasoning-oriented LLMs, this positions gradient-based optimization as an increasingly favorable paradigm. We release our codebase and GPT-5 traces at https://github.com/microsoft/RD-Agent.

cs.LG↗

arXiv2025

When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning

Functional tensor decomposition can analyze multi-dimensional data with real-valued indices, paving the path for applications in machine learning and signal processing. A limitation of existing approaches is the assumption that the tensor rank-a critical parameter governing model complexity-is known. However, determining the optimal rank is a non-deterministic polynomial-time hard (NP-hard) task and there is a limited understanding regarding the expressive power of functional low-rank tensor models for continuous signals. We propose a rank-revealing functional Bayesian tensor completion (RR-FBTC) method. Modeling the latent functions through carefully designed multioutput Gaussian processes, RR-FBTC handles tensors with real-valued indices while enabling automatic tensor rank determination during the inference process. We establish the universal approximation property of the model for continuous multi-dimensional signals, demonstrating its expressive power in a concise format. To learn this model, we employ the variational inference framework and derive an efficient algorithm with closed-form updates. Experiments on both synthetic and real-world datasets demonstrate the effectiveness and superiority of the RR-FBTC over state-of-the-art approaches. The code is available at https://github.com/OceanSTARLab/RR-FBTC.

cs.LG↗

arXiv2025

Less Is More: Generating Time Series with LLaMA-Style Autoregression in Simple Factorized Latent Spaces

Generative models for multivariate time series are essential for data augmentation, simulation, and privacy preservation, yet current state-of-the-art diffusion-based approaches are slow and limited to fixed-length windows. We propose FAR-TS, a simple yet effective framework that combines disentangled factorization with an autoregressive Transformer over a discrete, quantized latent space to generate time series. Each time series is decomposed into a data-adaptive basis that captures static cross-channel correlations and temporal coefficients that are vector-quantized into discrete tokens. A LLaMA-style autoregressive Transformer then models these token sequences, enabling fast and controllable generation of sequences with arbitrary length. Owing to its streamlined design, FAR-TS achieves orders-of-magnitude faster generation than Diffusion-TS while preserving cross-channel correlations and an interpretable latent space, enabling high-quality and flexible time series synthesis.

cs.LG↗

arXiv2025

R&D-Agent: An LLM-Agent Framework Towards Autonomous Data Science

Recent advances in AI and ML have transformed data science, yet increasing complexity and expertise requirements continue to hinder progress. Although crowd-sourcing platforms alleviate some challenges, high-level machine learning engineering (MLE) tasks remain labor-intensive and iterative. We introduce R&D-Agent, a comprehensive, decoupled, and extensible framework that formalizes the MLE process. R&D-Agent defines the MLE workflow into two phases and six components, turning agent design for MLE from ad-hoc craftsmanship into a principled, testable process. Although several existing agents report promising gains on their chosen components, they can mostly be summarized as a partial optimization from our framework's simple baseline. Inspired by human experts, we designed efficient and effective agents within this framework that achieve state-of-the-art performance. Evaluated on MLE-Bench, the agent built on R&D-Agent ranks as the top-performing machine learning engineering agent, achieving 35.1% any medal rate, demonstrating the ability of the framework to speed up innovation and improve accuracy across a wide range of data science applications. We have open-sourced R&D-Agent on GitHub: https://github.com/microsoft/RD-Agent.

cs.AI↗

arXiv2025

Functional Complexity-adaptive Temporal Tensor Decomposition

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by incorporating continuous timestamps in latent factors, they still struggle with general tensor data with continuous indexes not only in the temporal mode but also in other modes, such as spatial coordinates in climate data. Moreover, the challenge of self-adapting model complexity is largely unexplored in functional temporal tensor models, with existing methods being inapplicable in this setting. To address these limitations, we propose functional \underline{C}omplexity-\underline{A}daptive \underline{T}emporal \underline{T}ensor d\underline{E}composition (\textsc{Catte}). Our approach encodes continuous spatial indexes as learnable Fourier features and employs neural ODEs in latent space to learn the temporal trajectories of factors. To enable automatic adaptation of model complexity, we introduce a sparsity-inducing prior over the factor trajectories. We develop an efficient variational inference scheme with an analytical evidence lower bound, enabling sampling-free optimization. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that \textsc{Catte} not only reveals the underlying ranks of functional temporal tensors but also significantly outperforms existing methods in prediction performance and robustness against noise.

cs.LG↗

arXiv2025

Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations

Modeling and reconstructing multidimensional physical dynamics from sparse and off-grid observations presents a fundamental challenge in scientific research. Recently, diffusion-based generative modeling shows promising potential for physical simulation. However, current approaches typically operate on on-grid data with preset spatiotemporal resolution, but struggle with the sparsely observed and continuous nature of real-world physical dynamics. To fill the gaps, we present SDIFT, Sequential DIffusion in Functional Tucker space, a novel framework that generates full-field evolution of physical dynamics from irregular sparse observations. SDIFT leverages the functional Tucker model as the latent space representer with proven universal approximation property, and represents observations as latent functions and Tucker core sequences. We then construct a sequential diffusion model with temporally augmented UNet in the functional Tucker space, denoising noise drawn from a Gaussian process to generate the sequence of core tensors. At the posterior sampling stage, we propose a Message-Passing Posterior Sampling mechanism, enabling conditional generation of the entire sequence guided by observations at limited time steps. We validate SDIFT on three physical systems spanning astronomical (supernova explosions, light-year scale), environmental (ocean sound speed fields, kilometer scale), and molecular (organic liquid, millimeter scale) domains, demonstrating significant improvements in both reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.

cs.LG↗

arXiv2025

Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecasting

Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods. Deep learning (DL) models offer efficiency and accuracy but often ignore physical laws, limiting interpretability and generalization. We propose PhyDL-NWP, a physics-guided deep learning framework that integrates physical equations with latent force parameterization into data-driven models. It predicts weather variables from arbitrary spatiotemporal coordinates, computes physical terms via automatic differentiation, and uses a physics-informed loss to align predictions with governing dynamics. PhyDL-NWP enables resolution-free downscaling by modeling weather as a continuous function and fine-tunes pre-trained models with minimal overhead, achieving up to 170x faster inference with only 55K parameters. Experiments show that PhyDL-NWP improves both forecasting performance and physical consistency.

cs.LG↗

arXiv2025

MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model

Generative models aim to simulate realistic effects of various actions across different contexts, from text generation to visual effects. Despite significant efforts to build real-world simulators, the application of generative models to virtual worlds, like financial markets, remains under-explored. In financial markets, generative models can simulate complex market effects of participants with various behaviors, enabling interaction under different market conditions, and training strategies without financial risk. This simulation relies on the finest structured data in financial market like orders thus building the finest realistic simulation. We propose Large Market Model (LMM), an order-level generative foundation model, for financial market simulation, akin to language modeling in the digital world. Our financial Market Simulation engine (MarS), powered by LMM, addresses the domain-specific need for realistic, interactive and controllable order generation. Key observations include LMM's strong scalability across data size and model complexity, and MarS's robust and practicable realism in controlled generation with market impact. We showcase MarS as a forecast tool, detection system, analysis platform, and agent training environment, thus demonstrating MarS's "paradigm shift" potential for a variety of financial applications. We release the code of MarS at https://github.com/microsoft/MarS/.

q-fin.CP↗

arXiv2024

BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition

In real-world scenarios like traffic and energy, massive time-series data with missing values and noises are widely observed, even sampled irregularly. While many imputation methods have been proposed, most of them work with a local horizon, which means models are trained by splitting the long sequence into batches of fit-sized patches. This local horizon can make models ignore global trends or periodic patterns. More importantly, almost all methods assume the observations are sampled at regular time stamps, and fail to handle complex irregular sampled time series arising from different applications. Thirdly, most existing methods are learned in an offline manner. Thus, it is not suitable for many applications with fast-arriving streaming data. To overcome these limitations, we propose BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition. We treat the multivariate time series as the weighted combination of groups of low-rank temporal factors with different patterns. We apply a group of Gaussian Processes (GPs) with different kernels as functional priors to fit the factors. For computational efficiency, we further convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE), and developing a scalable algorithm for online inference. The proposed method can not only handle imputation over arbitrary time stamps, but also offer uncertainty quantification and interpretability for the downstream application. We evaluate our method on both synthetic and real-world datasets.We release the code at {https://github.com/xuangu-fang/BayOTIDE}

cs.LG↗

arXiv2024

Solving High Frequency and Multi-Scale PDEs with Gaussian Processes

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student $t$ mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at \url{https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE}.

cs.LG↗

arXiv2024

Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at \url{https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition}.

cs.LG↗

arXiv2023

Diffusion-Generative Multi-Fidelity Learning for Physical Simulation

Multi-fidelity surrogate learning is important for physical simulation related applications in that it avoids running numerical solvers from scratch, which is known to be costly, and it uses multi-fidelity examples for training and greatly reduces the cost of data collection. Despite the variety of existing methods, they all build a model to map the input parameters outright to the solution output. Inspired by the recent breakthrough in generative models, we take an alternative view and consider the solution output as generated from random noises. We develop a diffusion-generative multi-fidelity (DGMF) learning method based on stochastic differential equations (SDE), where the generation is a continuous denoising process. We propose a conditional score model to control the solution generation by the input parameters and the fidelity. By conditioning on additional inputs (temporal or spacial variables), our model can efficiently learn and predict multi-dimensional solution arrays. Our method naturally unifies discrete and continuous fidelity modeling. The advantage of our method in several typical applications shows a promising new direction for multi-fidelity learning.

cs.LG↗