Related papers: Accelerate Neural Subspace-Based Reduced-Order Sol…

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

In this paper, a restricted memory quasi-Newton bundle method for minimizing a locally Lipschitz continuous function over a Riemannian manifold is proposed. The curvature information of the objective function is approximated by applying a…

Neural implicit surfaces are a promising tool for geometry processing that represent a solid object as the zero level set of a neural network. Usually trained to approximate a signed distance function of the considered object, these methods…

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural…

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

Biophysical neural system simulations are among the most computationally demanding scientific applications, and their optimization requires navigating high-dimensional parameter spaces under numerous constraints that impose a binary…

Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…

Riemannian meta-optimization provides a promising approach to solving non-linear constrained optimization problems, which trains neural networks as optimizers to perform optimization on Riemannian manifolds. However, existing Riemannian…

We present an efficient spacetime optimization method to automatically generate animations for a general volumetric, elastically deformable body. Our approach can model the interactions between the body and the environment and automatically…

Accurate and efficient modeling of soft-tissue interactions is fundamental for advancing surgical simulation, surgical robotics, and model-based surgical automation. To achieve real-time latency, classical Finite Element Method (FEM)…

In this paper, we develop a low-order three-dimensional finite-element solver for fast multiple-case crust deformation analysis on GPU-based systems. Based on a high-performance solver designed for massively parallel CPU based systems, we…

Accurate simulation of brain deformation is a key component for developing realistic, interactive neurosurgical simulators, as complex nonlinear deformations must be captured to ensure realistic tool-tissue interactions. However,…

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…

This paper presents a novel methodology that uses surrogate models in the form of neural networks to reduce the computation time of simulation-based optimization of a reference trajectory. Simulation-based optimization is necessary when…

With the growing maturity of additive manufacturing, the fabrication of architected or lattice-based metamaterials has become a reality for industrial applications. These materials combine lightweight design with tailored mechanical…

Constrained motion planning is a common but challenging problem in robotic manipulation. In recent years, data-driven constrained motion planning algorithms have shown impressive planning speed and success rate. Among them, the latent…

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

As learned image compression (LIC) methods become increasingly computationally demanding, enhancing their training efficiency is crucial. This paper takes a step forward in accelerating the training of LIC methods by modeling the neural…

We study a class of optimization problems on Riemannian manifolds, where the objective function consists of a smooth term and quasi-norm type penalties with exponent $p \in (0, 1]$. The essential difficulty lies in the fact that the…