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Spatially varying image deblurring remains a fundamentally ill-posed problem, especially when degradations arise from complex mixtures of motion and other forms of blur under significant noise. State-of-the-art learning-based approaches…

Fast, accurate, and generalizable simulations are a key enabler of modern advances in robot design and control. However, existing simulation frameworks in robotics either model rigid environments and mechanisms only, or if they include…

In modern computer vision, the optimal representation of 3D shape continues to be task-dependent. One fundamental operation applied to such representations is differentiable rendering, as it enables inverse graphics approaches in learning…

Differentiable simulation establishes the mathematical foundation for solving challenging inverse problems in computer graphics and robotics, such as physical system identification and inverse dynamics control. However, rigor in frictional…

In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating $d$-dimensional piecewise continuous functions and for solving elliptic interface problems is developed. There are three novel features in the…

Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the…

We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Neural Radiance Fields (NeRF) have achieved remarkable progress in neural rendering. Extracting geometry from NeRF typically relies on the Marching Cubes algorithm, which uses a hand-crafted threshold to define the level set. However, this…

Neural Radiance Fields (NeRFs) have emerged as powerful tools for capturing detailed 3D scenes through continuous volumetric representations. Recent NeRFs utilize feature grids to improve rendering quality and speed; however, these…

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…

Neural implicit shape representations are an emerging paradigm that offers many potential benefits over conventional discrete representations, including memory efficiency at a high spatial resolution. Generalizing across shapes with such…

3D reconstruction of highly deformable surfaces (e.g. cloths) from monocular RGB videos is a challenging problem, and no solution provides a consistent and accurate recovery of fine-grained surface details. To account for the ill-posed…

This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…

Gradient descent prevails in artificial neural network training, but seems inept for spiking neural networks as small parameter changes can cause sudden, disruptive (dis-)appearances of spikes. Here, we demonstrate exact gradient descent…

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that…

Neural fields offer continuous, learnable representations that extend beyond traditional discrete formats in visual computing. We study the problem of learning neural representations of repeated antiderivatives directly from a function, a…

Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…