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We present an application of Physics-Informed Neural Networks to handle MultiPhase-Field simulations of microstructure evolution. It has been showcased that a combination of optimization techniques extended and adapted from the PINNs…

Neural Radiance Field training can be accelerated through the use of grid-based representations in NeRF's learned mapping from spatial coordinates to colors and volumetric density. However, these grid-based approaches lack an explicit…

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

We introduce Multiresolution Deep Implicit Functions (MDIF), a hierarchical representation that can recover fine geometry detail, while being able to perform global operations such as shape completion. Our model represents a complex 3D…

We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…

We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned…

Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

Temporally consistent surface reconstruction of dynamic 3D objects from unstructured point cloud data remains challenging, especially for very long sequences. Existing methods either optimize deformations incrementally, risking drift and…

We propose DynamicSurf, a model-free neural implicit surface reconstruction method for high-fidelity 3D modelling of non-rigid surfaces from monocular RGB-D video. To cope with the lack of multi-view cues in monocular sequences of deforming…

Implicit Neural Representations (INRs) have emerged as promising surrogates for large 3D scientific simulations due to their ability to continuously model spatial and conditional fields, yet they face a critical fidelity-speed dilemma: deep…

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…

Implicitly defined, continuous, differentiable signal representations parameterized by neural networks have emerged as a powerful paradigm, offering many possible benefits over conventional representations. However, current network…

We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our…

Neural signed distance functions (SDFs) are emerging as an effective representation for 3D shapes. State-of-the-art methods typically encode the SDF with a large, fixed-size neural network to approximate complex shapes with implicit…

This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated…

Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However,…

Constructing a high-quality dense map in real-time is essential for robotics, AR/VR, and digital twins applications. As Neural Radiance Field (NeRF) greatly improves the mapping performance, in this paper, we propose a NeRF-based mapping…