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Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…
Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively…
Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…
Research on control using models based on machine-learning methods has now shifted to the practical engineering stage. Achieving high performance and theoretically guaranteeing the safety of the system is critical for such applications. In…
We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…
Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…
The use of deep learning methods for modeling fluid flow has drawn a lot of attention in the past few years. In situations where conventional numerical approaches can be computationally expensive, these techniques have shown promise in…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…
Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…