Related papers: Parameter-Aware Ensemble SINDy for Interpretable S…

Discovering a meaningful symbolic expression that explains experimental data is a fundamental challenge in many scientific fields. We present a novel, open-source computational framework called Scientist-Machine Equation Detector (SciMED),…

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…

Symbolic regression (SR) is an emerging branch of machine learning focused on discovering simple and interpretable mathematical expressions from data. Although a wide-variety of SR methods have been developed, they often face challenges…

The recent focus on the efficiency of deep neural networks (DNNs) has led to significant work on model compression approaches, of which weight pruning is one of the most popular. At the same time, there is rapidly-growing computational…

Recently, information theoretic analysis has become a popular framework for understanding the generalization behavior of deep neural networks. It allows a direct analysis for stochastic gradient/Langevin descent (SGD/SGLD) learning…

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

Data-driven equation discovery aims to reconstruct governing equations directly from empirical observations. A fundamental challenge in this domain is the ill-posed nature of the inverse problem, where multiple distinct mathematical models…

In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing…

We introduce AI-Kolmogorov, a novel framework for Symbolic Density Estimation (SymDE). Symbolic regression (SR) has been effectively used to produce interpretable models in standard regression settings but its applicability to density…

We demonstrate that the stabilizer R\'{e}nyi entropy (SRE), a computable measure of quantum magic, can serve as an information-theoretic probe for universal properties associated with conformal defects in one-dimensional quantum critical…

In the context of population dynamics, identifying effective model features, such as fecundity and mortality rates, is generally a complex and computationally intensive process, especially when the dynamics are heterogeneous across the…

Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…

We extend the data-assimilation approach of Ling and Lozano-Dur\'an (AIAA 2025-1280) to develop machine-learning-based subgrid-scale stress (SGS) models for large-eddy simulation (LES) that are consistent with the numerical scheme of the…

In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and…

Semi-Supervised Instance Segmentation (SSIS) aims to leverage an amount of unlabeled data during training. Previous frameworks primarily utilized the RGB information of unlabeled images to generate pseudo-labels. However, such a mechanism…

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…

We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This…