Related papers: A comparative study of physics-informed neural net…

We propose a novel deep neural network (DNN) based approximation architecture to learn estimates of measurements. We detail an algorithm that enables training of the DNN. The DNN estimator only uses measurements, if and when they are…

Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…

Deep neural network (DNN) models have demonstrated impressive performance in various domains, yet their application in cognitive neuroscience is limited due to their lack of interpretability. In this study we employ two structurally…

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…

Dynamic response evaluation in structural engineering is the process of determining the response of a structure, such as member forces, node displacements, etc when subjected to dynamic loads such as earthquakes, wind, or impact. This is an…

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation…

Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…

Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…

This paper presents a physics-informed neural network (PINN) approach for monitoring the health of diesel engines. The aim is to evaluate the engine dynamics, identify unknown parameters in a "mean value" model, and anticipate maintenance…

The mathematical formulation of constitutive models to describe the path-dependent, i.e., inelastic, behavior of materials is a challenging task and has been a focus in mechanics research for several decades. There have been increased…

Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…

For many systems in science and engineering, the governing differential equation is either not known or known in an approximate sense. Analyses and design of such systems are governed by data collected from the field and/or laboratory…

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow…

Deep Neural Networks (DNNs) have been used to solve different day-to-day problems. Recently, DNNs have been deployed in real-time systems, and lowering the energy consumption and response time has become the need of the hour. To address…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Physics-informed neural networks are developed to characterize the state of dynamical systems in a random environment. The neural network approximates the probability density function (pdf) or the characteristic function (chf) of the state…