Related papers: Non-intrusive model reduction of large-scale, nonl…

We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a…

The backpropagation algorithm remains the dominant and most successful method for training deep neural networks (DNNs). At the same time, training DNNs at scale comes at a significant computational cost and therefore a high carbon…

The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover,…

Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation…

We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…

Compressive imaging aims to recover a latent image from under-sampled measurements, suffering from a serious ill-posed inverse problem. Recently, deep neural networks have been applied to this problem with superior results, owing to the…

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

As deep learning applications continue to deploy increasingly large artificial neural networks, the associated high energy demands are creating a need for alternative neuromorphic approaches. Optics and photonics are particularly compelling…

This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold…

Turbulent flow over permeable interface is omnipresent featuring complex flow topology. In this work, a data driven, end to end machine learning model has been developed to model the turbulent flow in porous media. For the same, we have…

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…

In this paper, we investigate data-driven parameterized modeling of insertion loss for transmission lines with respect to design parameters. We first show that direct application of neural networks can lead to non-physics models with…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…

Deep learning techniques have shown promise in many domain applications. This paper proposes a novel deep reservoir computing framework, termed deep recurrent stochastic configuration network (DeepRSCN) for modelling nonlinear dynamic…

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…