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In this paper we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we provide a comparison of our linear models with the classical…
Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape…
We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…
A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…
Simulation design is the choice of locations in parameter space at which simulations are to be run and is the first step in building an emulator capable of quickly providing estimates of simulation results for arbitrary locations in the…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
Two main approaches have been developed for learning first-order planning (action) models from unstructured data: combinatorial approaches that yield crisp action schemas from the structure of the state space, and deep learning approaches…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…
We propose a novel approach to image classification inspired by complex nonlinear biological visual processing, whereby classical convolutional neural networks (CNNs) are equipped with learnable higher-order convolutions. Our model…
Classical empirical force fields have dominated biomolecular simulation for over 50 years. Although widely used in drug discovery, crystal structure prediction, and biomolecular dynamics, they generally lack the accuracy and transferability…
The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…
A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…
Model order reduction seeks to approximate large-scale dynamical systems by lower-dimensional reduced models. For linear systems, a small reduced dimension directly translates into low computational cost, ensuring online efficiency. This…