Related papers: A parametric framework for kernel-based dynamic mo…

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely…

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),…

Laplace Neural Operators (LNOs) have recently emerged as a promising approach in scientific machine learning due to the ability to learn nonlinear maps between functional spaces. However, this framework often requires substantial amounts of…

We propose a deep reparametrization of the maximum a posteriori formulation commonly employed in multi-frame image restoration tasks. Our approach is derived by introducing a learned error metric and a latent representation of the target…

This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based…

Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with…

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

Low Rank Decomposition (LRD) is a model compression technique applied to the weight tensors of deep learning models in order to reduce the number of trainable parameters and computational complexity. However, due to high number of new…

Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not…

This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…

This work introduces a hybrid approach that combines the Proper Generalised Decomposition (PGD) with deep learning techniques to provide real-time solutions for parametrised mechanics problems. By relying on a tensor decomposition, the…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

This study introduces a surrogate modeling framework merging proper orthogonal decomposition, long short-term memory networks, and multi-task learning, to accurately predict elastoplastic deformations in real-time. Superior to single-task…

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…

Data-driven modeling of human motions is ubiquitous in computer graphics and computer vision applications, such as synthesizing realistic motions or recognizing actions. Recent research has shown that such problems can be approached by…

Scientific computing for large deformation of elastic-plastic solids is critical for numerous real-world applications. Classical numerical solvers rely primarily on local discrete linear approximation and are constrained by an inherent…

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…

Offline reinforcement learning (RL) aims to find a near-optimal policy using pre-collected datasets. In real-world scenarios, data collection could be costly and risky; therefore, offline RL becomes particularly challenging when the…