Related papers: Solving sign problems with physics-informed kernel…
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…
Numerically efficient and stable algorithms are essential for kernel-based regularized system identification. The state of art algorithms exploit the semiseparable structure of the kernel and are based on the generator representation of the…
The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields…
Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed…
Quantifying and propagating modeling uncertainties is crucial for reliability analysis, robust optimization, and other model-based algorithmic processes in engineering design and control. Now, physics-informed machine learning (PIML)…
In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…
Novel sampling algorithms can significantly impact open questions in computational biology, most notably the in silico protein folding problem. By using computational methods, protein folding aims to find the three-dimensional structure of…
Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…
We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and…
Robotic Information Gathering (RIG) relies on the uncertainty of a probabilistic model to identify critical areas for efficient data collection. Gaussian processes (GPs) with stationary kernels have been widely adopted for spatial modeling.…
Effective training of deep image segmentation models is challenging due to the need for abundant, high-quality annotations. Generating annotations is laborious and time-consuming for human experts, especially in medical image segmentation.…
Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…
Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…
Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…
This paper introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and sampling conditional on vertex strengths in weighted graphs. The algorithms can sample conditional on the…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
Nowadays, the coupling of electronic structure and machine learning techniques serves as a powerful tool to predict chemical and physical properties of a broad range of systems. With the aim of improving the accuracy of predictions, a large…
In this paper, we numerically examine the precision challenges that emerge in automatic differentiation and numerical integration in various tasks now tackled by physics-informed neural networks (PINNs). Specifically, we illustrate how…
Recently the use of neural networks has been introduced in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. This new technique has introduced…