Related papers: A Geometrical Method for Low-Dimensional Represent…
Modeling the dynamic behavior of deformable objects is crucial for creating realistic digital worlds. While conventional simulations produce high-quality motions, their computational costs are often prohibitive. Subspace simulation…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
We show that physics-based simulations can be seamlessly integrated with NeRF to generate high-quality elastodynamics of real-world objects. Unlike existing methods, we discretize nonlinear hyperelasticity in a meshless way, obviating the…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
This work presents a hybrid physics-informed and data-driven modeling framework for predictive control of autonomous off-road vehicles operating on deformable terrain. Traditional high-fidelity terramechanics models are often too…
Building upon recent developments of force-based estimators with a reduced variance for the computation of densities, radial distribution functions or local transport properties from molecular simulations, we show that the variance can be…
We derive a priori error estimates for the standard Galerkin and streamline diffusion finite element methods for the Fermi pencil-beam equation obtained from a fully three dimensional Fokker-Planck equation in space ${\mathbf x}=(x,y,z)$…
We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…
Simulations and inversions of electromagnetic geophysical data are paramount for discerning meaningful information about the subsurface from these data. Depending on the nature of the source electromagnetic experiments may be classified as…
We introduce a fast and invertible approximation for data simulated as 2D planar meshes with connectivities along the poloidal dimension in deforming 3D toroidal (donut-like) spaces generated by fusion simulations. In fusion simulations,…
High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…
Multi-fidelity models are of great importance due to their capability of fusing information coming from different numerical simulations, surrogates, and sensors. We focus on the approximation of high-dimensional scalar functions with low…
A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…
Our predictions for particle physics processes are realized in a chain of complex simulators. They allow us to generate high-fidelity simulated data, but they are not well-suited for inference on the theory parameters with observed data. We…
Bundle methods have been intensively studied for solving both convex and nonconvex optimization problems. In most of the bundle methods developed thus far, at least one quadratic programming (QP) subproblem needs to be solved in each…
We present a novel formulation for mesh-free, reduced-order simulation of deformable hyperelastic objects. Existing work in reduced-order elastodynamic simulation represents the input geometry by either meshes, which can be difficult to…
Neural simulation-based inference is a powerful class of machine-learning-based methods for statistical inference that naturally handles high-dimensional parameter estimation without the need to bin data into low-dimensional summary…