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A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be…
This paper presents a novel methodology for fast simulation and analysis of transient heat transfer. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
There are many challenges in bimanual assembly, including high-level sequencing, multi-robot coordination, and low-level, contact-rich operations such as component mating. Task and motion planning (TAMP) methods, while effective in this…
Tensor contraction operations in computational chemistry consume significant fractions of computing time on large-scale computing platforms. The widespread use of tensor contractions between large multi-dimensional tensors in describing…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
Federated learning (FL) is an emerging learning paradigm to tackle massively distributed data. In Federated Learning, a set of clients jointly perform a machine learning task under the coordination of a server. The FedAvg algorithm is one…
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical…
We demonstrate a practical differentiable programming approach for acoustic inverse problems through two applications: admittance estimation and shape optimization for resonance damping. First, we show that JAX-FEM's automatic…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…
We present a global optimizer, based on a conditional generative neural network, which can output ensembles of highly efficient topology-optimized metasurfaces operating across a range of parameters. A key feature of the network is that it…
We discuss the possibility to solve Modern Numerical Relativity problems using finite element methods (FEM). Adopting a "user friendly" software for handling totally general systems of nonlinear partial differential equations, FEMLAB, we…
Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…
Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…
Differentiable programming has emerged as a structural prerequisite for gradient-based inverse problems and end-to-end hybrid physics--machine learning in computational fluid dynamics. However, existing differentiable CFD platforms are…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
We present a Pseudo-Transient Topology Optimization (PeTTO) approach that can leverage graphics processing units (GPUs) to efficiently solve single-material and multi-material topology optimization problems. By integrating PeTTO with phase…