Related papers: Physics-Modeled Neural Networks
We introduce a unified theoretical framework for the rigorous analysis and systematic construction of deep neural networks (DNNs). This framework addresses a gap in existing theory by explicitly modeling the structure of tensor operations…
Deep Material Networks (DMNs) are structure-preserving, mechanistic machine learning models that embed micromechanical principles into their architectures, enabling strong extrapolation capabilities and significant potential to accelerate…
In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful…
Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in…
Accurate energy consumption forecasting is essential for efficient resource management and sustainability in the building sector. Deep learning models are highly successful but struggle with limited historical data and become unusable when…
Solving coupled systems of differential equations (DEs) is a central problem across scientific computing. While Physics Informed Neural Networks (PINNs) offer a promising, mesh-free approach, their standard architectures struggle with the…
Deep neural networks (DNNs) have proven to be highly effective in a variety of tasks, making them the go-to method for problems requiring high-level predictive power. Despite this success, the inner workings of DNNs are often not…
Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…
Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…
Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…
Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…
In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…
Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a…
In this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particular, we show that the use of special types of kernels yields…
Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each…
Deep neural networks (DNNs) have been widely used to solve partial differential equations (PDEs) in recent years. In this work, a novel deep learning-based framework named Particle Weak-form based Neural Networks (ParticleWNN) is developed…
Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…
This paper introduces Progressively Diffused Networks (PDNs) for unifying multi-scale context modeling with deep feature learning, by taking semantic image segmentation as an exemplar application. Prior neural networks, such as ResNet, tend…
In this work, we present a general purpose deep neural network package for representing energies, forces, dipole moments, and polarizabilities of atomistic systems. This so-called recursively embedded atom neural network model takes both…