arXiv subjects

Tingkai Xue

Publications and source records attributed to Tingkai Xue.

3 recordsLinked to original sources

arXiv2026

NeuralFVM: Neural-physics-based Finite Volume Method for Turbulent Flows Using the $k$-$\omega$ Model

In this work, we develop a neural-physics solver based on finite volume method (FVM), namely NeuralFVM, for turbulent flows by implementing the standard $k$-$\omega$ model designed for efficient Graphics Processing Unit (GPU) execution. The governing equations for fluid flow and heat transfer are reformulated as local tensor operations using convolution-based stencil operators, which enables compatibility with deep learning libraries while preserving the conservative properties of the FVM. A key challenge in implementing the turbulent model within such a framework is the treatment of the stiff destruction terms in the $k$ and $\omega$ transport equations. To address this issue, an operator-splitting strategy is introduced in which the stiff destruction terms are handled semi-implicitly while the remaining terms are advanced explicitly. This formulation avoids global matrix assembly and allows the entire solver to be implemented using local tensor operations. In addition, the pressure-velocity coupling is solved using a convolution-based geometric multigrid algorithm embedded within a neural network architecture. The resulting NeuralFVM solver is validated through comparison with simulations conducted using the commercial CFD software ANSYS Fluent for several channel-flow configurations and an indoor airflow scenario. The results demonstrate close agreement in velocity, temperature, and turbulence quantities, confirming the accuracy of the proposed approach. The developed GPU framework achieves a speedup of around 19-46 times compared with its Central Processing Unit (CPU) counterpart under different meshes. Moreover, the proposed solver naturally integrates with machine learning workflows, providing a promising foundation for future data-driven turbulence modeling and optimization.

physics.flu-dyn↗

arXiv2026

Physics-Informed Uncertainty Enables Reliable AI-driven Design

Inverse design is a central goal in much of science and engineering, including frequency-selective surfaces (FSS) that are critical to microelectronics for telecommunications and optical metamaterials. Traditional surrogate-assisted optimization methods using deep learning can accelerate the design process but do not usually incorporate uncertainty quantification, leading to poorer optimization performance due to erroneous predictions in data-sparse regions. Here, we introduce and validate a fundamentally different paradigm of Physics-Informed Uncertainty, where the degree to which a model's prediction violates fundamental physical laws serves as a computationally-cheap and effective proxy for predictive uncertainty. By integrating physics-informed uncertainty into a multi-fidelity uncertainty-aware optimization workflow to design complex frequency-selective surfaces within the 20 - 30 GHz range, we increase the success rate of finding performant solutions from less than 10% to over 50%, while simultaneously reducing computational cost by an order of magnitude compared to the sole use of a high-fidelity solver. These results highlight the necessity of incorporating uncertainty quantification in machine-learning-driven inverse design for high-dimensional problems, and establish physics-informed uncertainty as a viable alternative to quantifying uncertainty in surrogate models for physical systems, thereby setting the stage for autonomous scientific discovery systems that can efficiently and robustly explore and evaluate candidate designs.

cs.LG↗

arXiv2025

Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulations

Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This work presents a hybrid physics-neural model that predicts scalar transport in a complex domain orders of magnitude faster than the 3D simulation (from hours to less than 1 min). This end-to-end differentiable framework jointly learns the physical model parameterization (i.e. orthotropic diffusivity) and a non-Markovian neural closure model to capture unresolved, 'coarse-grained' effects, thereby enabling stable, long time horizon rollouts. This proposed model is data-efficient (learning with 26 training data), and can be flexibly extended to an out-of-distribution scenario (with a moving source), achieving a Spearman correlation coefficient of 0.96 at the final simulation time. Overall results show that this differentiable physics-neural framework enables fast, accurate, and generalizable coarse-grained surrogates for physical phenomena.

physics.comp-ph↗