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Crystal plasticity finite element model (CPFEM) is a powerful numerical simulation in the integrated computational materials engineering (ICME) toolboxes that relates microstructures to homogenized materials properties and establishes the…
We consider the problem of inferring latent stochastic differential equations (SDEs) with a time and memory cost that scales independently with the amount of data, the total length of the time series, and the stiffness of the approximate…
This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…
Achieving optimal rates for stochastic composite convex optimization without prior knowledge of problem parameters remains a central challenge. In the deterministic setting, the auto-conditioned fast gradient method has recently been…
Energy-based finite-element formulations provide a unified framework for describing complex physical systems in computational mechanics. In these energy-based methods, the governing equations can be obtained directly by considering the…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
In this paper, elliptic control problems with pointwise box constraints on the state is considered, where the corresponding Lagrange multipliers in general only represent regular Borel measure functions. To tackle this difficulty, the…
We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…
We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a…
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…
Disentanglement is a useful property in representation learning which increases the interpretability of generative models such as Variational autoencoders (VAE), Generative Adversarial Models, and their many variants. Typically in such…
Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
Crystal plasticity models are a powerful tool for predicting the deformation behaviour of polycrystalline materials accounting for the underlying grain morphology and texture. These models typically have a large number of parameters, an…
The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator…
Neuronal damage, in the form of both brain and spinal cord injuries, is one of the major causes of disability and death in young adults worldwide. One way to assess the direct damage occurring after a mechanical insult is the simulation of…
Advances in manufacturing and characterization of complex molecular systems have created a need for new methods for design at molecular length scales. Emerging approaches are increasingly relying on the use of Artificial Intelligence (AI),…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
Aggregative cooperative optimization problems arise in distributed decision-making settings where each agent's objective depends on its own decision as well as on an aggregate variable capturing global system behavior. Motivated by…