7 papers
A Streaming Sparse Cholesky Method for Derivative-Informed Gaussian Process Surrogates Within Digital Twin Applications
Shridhar Vashishtha, Krishna Prasath Logakannan, Jacob Hochhalter +2
Digital twins are developed to model the behavior of a specific physical asset (or twin), and they can consist of high-fidelity physics-based models or surrogates. A highly accurat…
Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients
Zachary Bastiani, Robert M. Kirby, Jacob Hochhalter +1
We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the p…
HyResPINNs: A Hybrid Residual Physics-Informed Neural Network Architecture Designed to Balance Expressiveness and Trainability
Madison Cooley, Robert M. Kirby, Shandian Zhe +1
Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that…
SIFBench: An Extensive Benchmark for Fatigue Analysis
Tushar Gautam, Robert M. Kirby, Jacob Hochhalter +1
Fatigue-induced crack growth is a leading cause of structural failure across critical industries such as aerospace, civil engineering, automotive, and energy. Accurate prediction o…
Diffusion-Based Symbolic Regression
Zachary Bastiani, Robert M. Kirby, Jacob Hochhalter +1
Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress,…
Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases
Madison Cooley, Varun Shankar, Robert M. Kirby +1
Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs…