Related papers: Solving sign problems with physics-informed kernel…
Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…
We present a new method for design problems wherein the goal is to maximize or specify the value of one or more properties of interest. For example, in protein design, one may wish to find the protein sequence that maximizes fluorescence.…
We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where…
We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear…
Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…
Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its…
Efficient and easy segmentation of images and volumes is of great practical importance. Segmentation problems that motivate our approach originate from microscopy imaging commonly used in materials science, medicine, and biology. We…
We present a physics-informed machine-learning (PIML) approach for the approximation of slow invariant manifolds (SIMs) of singularly perturbed systems, providing functionals in an explicit form that facilitate the construction and…
Kernel methods have been proven to be a powerful tool for the integration and analysis of highthroughput technologies generated data. Kernels offer a nonlinear version of any linear algorithm solely based on dot products. The kernelized…
Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in…
Assigning weights to a large pool of objects is a fundamental task in a wide variety of applications. In this article, we introduce the concept of structured high-dimensional probability simplexes, in which most components are zero or near…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
Graphs are useful to interpret widely used image processing methods, e.g., bilateral filtering, or to develop new ones, e.g., kernel based techniques. However, simple graph constructions are often used, where edge weight and connectivity…
This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based…
Radiation heat transfer in a graded-index medium often suffers accuracy problems due to the gradual changes in the refractive index. The finite element method, meshfree, and other numerical methods often struggle to maintain accuracy when…
Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…
Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…
A fundamental problem on graph-structured data is that of quantifying similarity between graphs. Graph kernels are an established technique for such tasks; in particular, those based on random walks and return probabilities have proven to…