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Microstructural heterogeneity affects the macro-scale behavior of materials. Conversely, load distribution at the macro-scale changes the microstructural response. These up-scaling and down-scaling relations are often modeled using…
Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…
The dynamics of materials failure is one of the most critical phenomena in a range of scientific and engineering fields, from healthcare to structural materials to transportation. In this paper we propose a specially designed deep neural…
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…
A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward…
Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…
Numerical simulation of nonlinear elastic wave propagation in solids with cracks is indispensable for decoding the complicated mechanisms associated with the nonlinear ultrasonic techniques in Non-Destructive Testing (NDT). Here, we…
This dissertation addresses two aspects of the theory and simulation of stress-diffusion coupling in semiconductors. The first part is a study of the role of kinetics in the formation of pits in stressed thin films. The second part…
The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and…
In the field of brittle fracture animation, generating realistic destruction animations using physics-based simulation methods is computationally expensive. While techniques based on Voronoi diagrams or pre-fractured patterns are effective…
Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward…
Evaluating the mechanical response of fiber-reinforced composites can be extremely time consuming and expensive. Machine learning (ML) techniques offer a means for faster predictions via models trained on existing input-output pairs and…
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
Underwater explosions produce complex fluid phenomena relevant to diverse applications including maritime engineering, medical therapeutics, and inertial confinement fusion. These systems exhibit multiphase flows, chemical kinetics, and…
Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs) offer a highly expressive and flexible framework for modeling complex…
We propose a framework for training neural networks that are coupled with partial differential equations (PDEs) in a parallel computing environment. Unlike most distributed computing frameworks for deep neural networks, our focus is to…
Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…
An important task in structural design is to quantify the structural performance of an object under the external forces it may experience during its use. The problem proves to be computationally very challenging as the external forces'…
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…
For ensuring vehicle safety, the impact performance of wheels during wheel development must be ensured through a wheel impact test. However, manufacturing and testing a real wheel requires a significant time and money because developing an…