Related papers: Finite Element Network Analysis: A Machine Learnin…

We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function…

In this paper, we address the design of lightweight deep learning-based edge detection. The deep learning technology offers a significant improvement on the edge detection accuracy. However, typical neural network designs have very high…

Most currently available methods for modeling multiphysics, including thermoelasticity, using machine learning approaches, are focused on solving complete multiphysics problems using data-driven or physics-informed multi-layer perceptron…

We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…

Deep neural networks achieve remarkable performance in many computer vision tasks. Most state-of-the-art (SOTA) semantic segmentation and object detection approaches reuse neural network architectures designed for image classification as…

Simulating complex unsteady physical phenomena relies on detailed mathematical models, simulated for instance by using the Finite Element Method (FEM). However, these models often exhibit discrepancies from the reality due to unmodeled…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously…

Quantum-mechanics-based transport simulation is of importance for the design of ultra-short channel field-effect transistors (FETs) with its capability of understanding the physical mechanism, while facing the primary challenge of the high…

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

In this paper, we study a machine-learning-based solver for high-dimensional partial differential equations (PDEs). Computing accurate solutions efficiently for such problems remains challenging because of the curse of dimensionality, which…

We introduce an end-to-end computational framework that allows for hyperparameter optimization using the DeepHyper library, accelerated model training, and interpretable AI inference. The framework is based on state-of-the-art AI models…

We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate…

Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve…

The widespread success of foundation models in natural language processing and computer vision has inspired researchers to extend the concept to scientific machine learning and computational science. However, this position paper argues that…

This paper investigates the problem of network embedding, which aims at learning low-dimensional vector representation of nodes in networks. Most existing network embedding methods rely solely on the network structure, i.e., the linkage…

In this paper, we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations (PDEs). The main idea is to use a neural network to learn the…

Classically, the constitutive behavior of materials is described either phenomenologically, or by homogenization approaches. Phenomenological approaches are computationally very efficient, but are limited for complex non-linear and…

AdaNet is a lightweight TensorFlow-based (Abadi et al., 2015) framework for automatically learning high-quality ensembles with minimal expert intervention. Our framework is inspired by the AdaNet algorithm (Cortes et al., 2017) which learns…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…