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We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determined alongside other unknown physical parameters and the…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
Physics-inspired regularization is desired for intra-patient image registration since it can effectively capture the biomechanical characteristics of anatomical structures. However, a major challenge lies in the reliance on physical…
This article aims to present a general analysis of a class of inverse problems that consists in recovering the elliptic parameter maps in systems of PDEs, such as the linear elastic system, from the knowledge of some of their solutions.…
This work addresses the inverse identification of apparent elastic properties of random heterogeneous materials using machine learning based on artificial neural networks. The proposed neural network-based identification method requires the…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…
Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…
The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and…
This paper investigates both biomechanical-constrained non-rigid medical image registrations and accurate identifications of material properties for soft tissues, using physics-informed neural networks (PINNs). The complex nonlinear…
Soft biological tissues often have complex mechanical properties due to variation in structural components. In this paper, we develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) to infer the spatial…
We learn parameterized nonlinear elasticity on curved surfaces using a physics-informed neural network that enforces governing equations and boundary conditions directly through the loss function, enabling a single trained model to…
An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a…
Parameter estimation in structural dynamics generally involves inferring the values of physical, geometric, or even customized parameters based on first principles or expert knowledge, which is challenging for complex structural systems. In…
Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…
Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…
In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently…
Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate…
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…