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This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the…

A meta-model (or a surrogate model) is the modern name for what was traditionally called a response surface. It is intended to mimic the behaviour of a computational model M (e.g. a finite element model in mechanics) while being inexpensive…

We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…

This paper puts forward an integrated microstructure design methodology that replaces the common existing design approaches: 1) reconstruction of microstructures, 2) analyzing and quantifying material properties, and 3) inverse design of…

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

This paper concerns the distributed training of nonlinear kernel machines on Map-Reduce. We show that a re-formulation of Nystr\"om approximation based solution which is solved using gradient based techniques is well suited for this,…

Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive…

Recent work has focused on combining kernel methods and deep learning to exploit the best of the two approaches. Here, we introduce a new architecture of neural networks in which we replace the top dense layers of standard convolutional…

Simulating the time evolution of physical systems is pivotal in many scientific and engineering problems. An open challenge in simulating such systems is their multi-resolution dynamics: a small fraction of the system is extremely dynamic,…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

When repeated evaluations for varying parameter configurations of a high-fidelity physical model are required, surrogate modeling techniques based on model order reduction are desired. In absence of the governing equations describing the…

Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…

This study presents a methodology to treat performance-based seismic design as an inverse engineering problem, where design parameters are directly derived to achieve specific performance objectives. By implementing explainable machine…

Thanks to their versatility, ease of deployment and high-performance, surrogate models have become staple tools in the arsenal of uncertainty quantification (UQ). From local interpolants to global spectral decompositions, surrogates are…

It is not uncommon that meta-heuristic algorithms contain some intrinsic parameters, the optimal configuration of which is crucial for achieving their peak performance. However, evaluating the effectiveness of a configuration is expensive,…

We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and…

This paper presents a novel methodology that uses surrogate models in the form of neural networks to reduce the computation time of simulation-based optimization of a reference trajectory. Simulation-based optimization is necessary when…

Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…