Related papers: BubbleOKAN: A Physics-Informed Interpretable Neura…

We introduce a novel physics-informed approach for accurately modeling aggregation kinetics which provides a comprehensive solution in a single run by outputting all model parameters simultaneously, a clear advancement over traditional…

Uncovering physical laws from experimental data is a fundamental goal of theoretical physics. In this work, we apply the spline-based, interpretable Kolmogorov-Arnold Network (KAN) to explore the algebraic structure underlying the baryon…

Accurate segmentation of individual teeth from panoramic radiographs remains a challenging task due to anatomical variations, irregular tooth shapes, and overlapping structures. These complexities often limit the performance of conventional…

Despite their immense success, deep convolutional neural networks (CNNs) can be difficult to optimize and costly to train due to hundreds of layers within the network depth. Conventional convolutional operations are fundamentally limited by…

Physics-Informed Neural Networks (PINNs) and more recently Physics-Informed Kolmogorov-Arnold Networks (PIKANs) have emerged as promising approaches for solving partial differential equations (PDEs) without reliance on extensive labeled…

Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design…

Accurate knowledge of acoustic surface admittance or impedance is essential for reliable wave-based simulations, yet its in situ estimation remains challenging due to noise, model inaccuracies, and restrictive assumptions of conventional…

Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…

Modeling boiling (an inherently chaotic, multiphase process central to energy and thermal systems) remains a significant challenge for neural PDE surrogates. Existing models require future input (e.g., bubble positions) during inference…

Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are…

We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in…

Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful alternative to traditional multilayer perceptrons. However, their reliance on predefined, bounded grids restricts their ability to approximate functions on unbounded…

We propose a Deep Operator Network~(DeepONet) framework to learn the dynamic response of continuous-time nonlinear control systems from data. To this end, we first construct and train a DeepONet that approximates the control system's local…

Thrombosis involves processes spanning large-scale fluid flow to sub-cellular events such as platelet activation. Traditional CFD approaches often treat blood as a continuum, which can limit their ability to capture these microscale…

Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…

Accurate prediction of blast pressure fields is essential for applications in structural safety, defense planning, and hazard mitigation. Traditional methods such as empirical models and computational fluid dynamics (CFD) simulations offer…

In this work, we propose a modified Hybrid Parallel Kolmogorov--Arnold Network and Multilayer Perceptron Physics-Informed Neural Network to overcome the high-frequency and multiscale challenges inherent in Physics-Informed Neural Networks.…

Solving partial differential equations (PDEs) is essential in scientific forecasting and fluid dynamics. Traditional approaches often incur expensive computational costs and trade-offs in efficiency and accuracy. Recent deep neural networks…

Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational…