arXiv subjects

Guanyu Pan

Publications and source records attributed to Guanyu Pan.

4 recordsLinked to original sources

arXiv2026

Stable Fine-Time-Step Long-Horizon Turbulence Prediction with a Multi-Stepsize Mixture-of-Experts Neural Operator

Neural operators have been increasingly used as data-driven surrogates for time-marching predictions of turbulent flows. However, long-horizon autoregressive prediction is sensitive to error accumulation and the choice of prediction interval. Excessively small time increments may increase temporal redundancy and lengthen rollouts, which can degrade the stability of neural operators in turbulence forecasting. This work pursues a unified objective: stable long-horizon autoregressive prediction at fine temporal resolution for three-dimensional turbulence. We propose a multi-stepsize mixture-of-experts (Ms-MoE) neural operator built on an implicit factorized Transformer (IFactFormer) backbone. The model conditions on a requested relative stride and uses a time-step router to activate scale-specific routed experts together with a shared expert, yielding a single architecture that represents a family of stride-parameterized time-advancement operators. We evaluate the approach on forced homogeneous isotropic turbulence (HIT) and turbulent channel flow using filtered direct numerical simulation datasets. Relative to sampling intervals used in previous studies, we construct training datasets with up to 20 times finer temporal resolution and report long-horizon autoregressive rollouts using qualitative time-slice comparisons and long-time-averaged statistics. Ms-MoE-IFactFormer yields more stable long-horizon rollouts and improved agreement with long-time-averaged statistics on both HIT and turbulent channel flow, suggesting potential for stable time-marching at fine temporal resolution in more complex turbulent flows.

physics.flu-dyn↗

arXiv2025

Transcending Sparse Measurement Limits: Operator-Learning-Driven Data Super-Resolution for Inverse Source Problem

Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Direct Sampling Method). We present a modular framework that significantly improves multi-source localization from extremely sparse single-frequency measurements. First, we extend a uniqueness theorem for the inverse source problem, proving that a unique solution is guaranteed under limited viewing apertures. Second, we employ a Deep Operator Network (DeepONet) with a branch-trunk architecture to interpolate the sparse measurements, lifting six to ten samples within the narrow aperture to a sufficiently dense synthetic aperture. Third, the super-resolved field is fed into the Direct Sampling Method (DSM). For a single source, we derive an error estimate showing that sparse data alone can achieve grid-level precision. In two- and three-source trials, localization from raw sparse measurements is unreliable, whereas DeepONet-reconstructed data reduce localization error by about an order of magnitude and remain effective with apertures as small as $\pi/4$. By decoupling interpolation from inversion, the framework allows the interpolation and inversion modules to be swapped with neural operators and classical algorithms, respectively, providing a practical and flexible design that improves localization accuracy compared with standard baselines.

math.NA↗

arXiv2025

Inverse Problems for Partial Differential Equations with Jump Discontinuities in Coefficients via Two-Stage Physics-Informed Deep Learning and Statistical Mixture Models

This work proposes a two-stage physics-informed deep learning framework that combines neural-network-based sampling with statistical inference and constrained parameter refinement. In the first stage, a dual-network physics-informed architecture is used, where a main network approximates the PDE solution and an auxiliary coefficient sub network provides a relaxed continuous surrogate of the true discontinuous coefficient field. A gradient-adaptive weighting strategy is incorporated into the physics residual to improve residual training and enhance sampling reliability near possible discontinuity regions. The sampled coefficient values are then analyzed using Bayesian learning for Gaussian mixture models and birth-death Markov chain model selection, which estimate the number of coefficient regimes and provide heuristic search intervals for coefficient values and candidate transition regions. In the second stage, the inverse problem is reformulated as a constrained physics-informed estimator, in which the coefficient is represented explicitly as a hard piecewise-constant function over the spatiotemporal domain. Numerical experiments on different PDE types with jump-discontinuous coefficients demonstrate that the proposed framework achieves accurate parameter estimation with acceptable computational costs compared to existing methods. This work provides an effective integrated workflow for inverse problems governed by PDEs with discontinuous parameter structures, particularly in nonstationary and heterogeneous systems.

stat.ML↗

arXiv2023

Parameter Identification for Partial Differential Equations with Spatiotemporal Varying Coefficients

To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the resolution of the parameter inverse problem from the observed spatiotemporal data a challenging endeavor. Starting from the observed data obtained from such systems, we propose a novel framework that facilitates the investigation of parameter identification for multi-state systems governed by spatiotemporal varying parametric partial differential equations. Our framework consists of two integral components: a constrained self-adaptive physics-informed neural network, encompassing a sub-network, as our methodology for parameter identification, and a finite mixture model approach to detect regions of probable parameter variations. Through our scheme, we can precisely ascertain the unknown varying parameters of the complex multi-state system, thereby accomplishing the inversion of the varying parameters. Furthermore, we have showcased the efficacy of our framework on two numerical cases: the 1D Burgers' equation with time-varying parameters and the 2D wave equation with a space-varying parameter.

cs.LG↗