Related papers: Non-intrusive Surrogate Modeling for Parametrized …

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…

Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and…

We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…

In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…

Finite Element Analysis (FEA) is a powerful but computationally intensive method for simulating physical phenomena. Recent advancements in machine learning have led to surrogate models capable of accelerating FEA. Yet there are still…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer…

Machine learning models of accelerator systems (`surrogate models') are able to provide fast, accurate predictions of accelerator physics phenomena. However, approaches to date typically do not include measured input diagnostics, such as…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains,…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

It has been shown that cooperative coevolution (CC) can effectively deal with large scale optimization problems (LSOPs) through a divide-and-conquer strategy. However, its performance is severely restricted by the current…

Most practical engineering design problems involve nonlinear spatio-temporal dynamical systems. Multi-physics simulations are often performed to capture the fine spatio-temporal scales which govern the evolution of these systems. However,…

We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

This work presents a data-driven framework for fast forward and inverse analysis in topology optimization (TO) by combining Rank Reduction Autoencoders (RRAEs) with neural latent-space mappings. The methodology targets the efficient…

We build surrogate models for dynamic 3D subsurface single-phase flow problems with multiple vertical producing wells. The surrogate model provides efficient pressure estimation of the entire formation at any timestep given a stochastic…

We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in…

We address a three-tier data-driven approach to solve the inverse problem in complex systems modelling from spatio-temporal data produced by microscopic simulators using machine learning. In the first step, we exploit manifold learning and…