Differentiable voxelization for 3D meshes with GPU acceleration.
problem Efficient and accurate voxelization of 3D meshes.
method Differentiable voxelization using winding number and solid angles, with GPU acceleration and neural network deformation.
result State-of-the-art performance in accuracy and efficiency on the ShapeNet dataset.
CupNet prunes neural nets for cup-shaped data.
problem Pruning neural networks for cup-shaped data.
method Used simulated cup drawing data to prune a neural network.
result Pruning effectively reduces network size for cup-shaped data.
Eliciting semantic similarity between concepts in the biomedical domain remains a challenging task. Recent approaches founded on embedding vectors have gained in popularity as they risen to efficiently capture semantic relationships The underlying idea is that two words that have close meaning gather similar contexts. …
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networ…
A CNN on semi-regular meshes classifies brain diseases from MRI scans.
problem Classifying brain diseases from MRI scans.
method Developed a vertex-based graph CNN for semi-regular triangulated meshes.
result Vertex-based graph CNN outperformed spectral graph CNN in classifying MCI and AD.
Paper introduces MNNs for efficient neural network training.
problem Training large-scale sparse neural networks efficiently.
method Formal derivation of MNN architecture with forward-only gradient propagation.
result MNNs can efficiently compute gradients without backward computation.
A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of inform…
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
Generative model creates high-quality meshes from point clouds.
problem Creating accurate meshes from point cloud data.
method Modeling point cloud generation as sphere deformation through deep neural networks.
result The model efficiently generates high-quality meshes from point clouds.
Physics-guided deep learning improves CFD for bubbly flow simulations.
problem Accurate CFD prediction of two-phase bubbly flow with high computational efficiency.
method Developed a multi-scale framework with Feature Similarity Measurement (FSM) for error estimation and a physics-guided deep feedforward neural network (DFNN) surrogate model.
result Physics-guided deep learning achieves comparable accuracy to fine-mesh simulations with fast-running feature.
Neural net solves PDEs without labels, useful for EIT.
problem Solving PDEs for electrical impedance tomography.
method Unsupervised deep learning with neural network minimizer.
result Deep neural network approximates PDE solutions.
New method uses dynamic sampling to improve PINNs efficiency.
problem Improving sample efficiency and performance of PINNs.
method pdPINN, inspired by Eulerian formulation, uses dynamic Monte Carlo sampling from particle positions.
result Higher sample efficiency and improved performance of PINNs.
Automates design of lightweight neural networks for image classification.
problem Designing efficient neural networks for edge devices with limited computational resources.
method Uses the Mesh Adaptive Direct Search (MADS) algorithm to optimize network architecture.
result Achieves comparable performance to standard methods with fewer design trials.
GeONet learns the Wasserstein geodesic without mesh discretization.
problem Computing the Wasserstein geodesic between complex data distributions.
method Mesh-invariant deep neural operator network that learns saddle point optimality conditions.
result GeONet achieves comparable accuracy to standard OT solvers with reduced computational cost.
Batch-splitting (data-parallelism) is the dominant distributed Deep Neural Network (DNN) training strategy, due to its universal applicability and its amenability to Single-Program-Multiple-Data (SPMD) programming. However, batch-splitting suffers from problems including the inability to train very large models (due to…
Neural networks are based on a simplified model of the brain. In this project, we wanted to relax the simplifying assumptions of a traditional neural network by making a model that more closely emulates the low level interactions of neurons. Like in an RNN, our model has a state that persists between time steps, so tha…
PolyGen models 3D meshes directly, predicting vertices and faces sequentially.
problem Efficiently modeling 3D geometry for computer graphics, robotics, and games.
method Transformer-based autoregressive model for predicting mesh vertices and faces.
result PolyGen produces high-quality, usable 3D meshes and competitive conditional performance.
In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a prior for the coefficient to be estimated from noisy data. Neural networks are global, smooth function approximators and as such they do not require explicit regularization of the er…
Novel neural operator predicts complex spatiotemporal dynamics from partial observations.
problem Capturing complex operator dynamics in infinite-dimensional function spaces.
method Integrates Koopman operator theory with deep neural networks to approximate nonlinear operators between Banach spaces.
result BNO achieves robust zero-shot super-resolution in unsteady flow prediction and outperforms conventional methods.
A mesh-free method solves continuum-marginal optimal transport problems.
problem Recovering minimum-energy velocity fields from time-continuous probability marginals.
method Embeds weak continuity equation in a reproducing kernel Hilbert space, optimizing with mini-batch stochastic methods.
result Accurately recovers drift and maintains marginal consistency in synthetic experiments.
New mesh network preserves symmetries in deep learning.
problem No existing mesh processing architecture is equivariant to all symmetries.
method Equivariant attention-based mesh network using relative tangential features.
result The network achieves improved performance and is equivariant to various transformations.
Proposes a new CNN for meshes that can handle orientation.
problem Isotropic kernels in graph convolutions are insensitive to mesh geometry.
method Introduces gauge equivariant kernels and geometric message passing.
result Significantly improved expressivity over conventional GCNs.
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since mesh…
Proposes polynomial neural networks for improved function approximation in various tasks.
problem Improving function approximation in various tasks like image generation, face verification, and 3D mesh representation learning.
method Introduces polynomial neural networks (Π-Nets) and three tensor decompositions to reduce parameter count and enhance expressiveness. result Demonstrates that Π-Nets can produce state-of-the-art results in challenging tasks without non-linear activation functions. Neural Q-learning tackles high-dimensional PDEs.
problem Solving high-dimensional PDEs is computationally challenging.
method Adapting Q-learning from reinforcement learning to solve PDEs.
result The neural network approximator converges to the PDE solution as the network width increases.
Instantiation-Net reconstructs 3D mesh from single 2D image for right ventricle.
problem Reconstructing 3D shape from limited 2D images for surgical navigation.
method Combines DCNN for feature extraction and GCN for mesh reconstruction.
result Demonstrates practical strength and potential clinical use.
New Gaussian priors for neural networks improve scalability and Bayesian inference stability.
problem Scalability and stability issues in Bayesian neural network inference.
method Introduces a new Gaussian neural network prior with decreasing variance in network width, enabling stable MCMC sampling.
result The new prior enables stable MCMC sampling for Bayesian neural network inference, improving scalability and stability.
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the network output with respect to the space variables which is needed to approxima…
PointTriNet generates 3D triangulations from point clouds efficiently and scalably.
problem Generating a triangulation among a set of points in 3D space.
method Iteratively applies a classification network and a proposal network over nearby points and triangles, using a novel triangle-relative input encoding.
result Generates robust and scalable triangulations for 3D learning pipelines.
Highly expressive models such as deep neural networks (DNNs) have been widely applied to various applications. However, recent studies show that DNNs are vulnerable to adversarial examples, which are carefully crafted inputs aiming to mislead the predictions. Currently, the majority of these studies have focused on per…
A neural network method tackles high-dimensional diffeomorphic mapping problems.
problem High-dimensional diffeomorphic mapping struggles with the curse of dimensionality.
method Combines variational principles with quasi-conformal theory for accurate, bijective mappings.
result Validated accuracy, robustness, and effectiveness in complex registration scenarios.
GIT-Net uses neural networks to approximate PDE operators efficiently.
problem Approximating PDE operators for complex geometries.
method Parametrizes adaptive generalized integral transforms with deep neural networks.
result GIT-Net outperforms existing neural network operators in multiple areas.
Neural network solves BVPs with unstructured data.
problem Solving Boundary Value Problems (BVPs) with numerical methods.
method Neural Network based numerical method for solving BVPs.
result Validated the method for Laplace and Poisson equations.
In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any 3x3-mesh made of quadran…
Hydrogen atom confined in an inverted-Gaussian potential, with detailed numerical methods and results.
problem Studying hydrogen atom in a specific potential.
method Three numerical methods: Lagrange-mesh, fourth order finite differences, and finite element method.
result Accurate numerical results for hydrogen atom energies and eigenfunctions, improving previous literature.
We create a smooth manifold of triangular meshes with a geodesically complete metric.
problem Representing and manipulating 2D shapes as triangular meshes.
method Developed a geodesically complete Riemannian metric for triangular meshes.
result The metric preserves mesh connectivity and avoids mesh degradation.
New neural network solves Nirenberg problem for curvature on sphere.
problem Prescribing Gaussian curvature on S2 for metrics conformal to the round metric. method Mesh-free physics-informed neural network (PINN) that directly parametrises the conformal factor.
result Neural network achieves very low losses for realisable curvatures, distinguishing them from non-realisable ones.
Generalized meshes for non-regular geometries, including fractures.
problem Discretization of partial differential equations in non-regular geometries.
method Introduces generalized meshes with overlapping elements and flexible adjacency relations.
result Discrete differential forms on virtually inflated meshes characterize the trace space of forms in surrounding volumes.
Proposes CXNs for neural network computations on cell complexes.
problem Performing neural network computations on complex topological spaces.
method Introduces a message passing scheme and a unified encoder-decoder framework for cell complexes.
result Generalizes message passing to cell complexes and provides a cell2vec representation.
DGNet solves complex dynamical systems with neural networks and constraints.
problem Real-time accurate solutions for large-scale complex systems.
method Model-constrained discontinuous Galerkin Network (DGNet) for compressible Euler equations.
result DGNet achieves out-of-distribution generalization and improved stability.
We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants, which learn…
New method improves human mesh recovery for obese people.
problem Improving mesh recovery for obese people.
method Generative optimization of mesh parameters from 2D keypoints.
result Significant improvement in mesh recovery performance on obese person images.
Graph convolutional Gaussian processes learn functions on graphs.
problem Learning translation-invariant relationships on non-Euclidean domains.
method Bayesian nonparametric method using graph convolutional neural networks.
result Graph convolutional Gaussian processes outperform existing methods on images and triangular meshes.
Extends geometric decompositions to arbitrary meshes and forms.
problem Constructing local bases for finite element spaces on arbitrary meshes.
method Generalizes extension operators to arbitrary meshes and forms, showing they yield geometric decompositions.
result Extension operators yield geometric decompositions for arbitrary meshes and forms.
The paper explores the topology of polygonal meshes and their properties.
problem Understanding the topological properties of polygonal meshes.
method Overview of topological concepts, definitions of intrinsic and extrinsic topology, proofs of Euler and Euler-Poincaré formulas, and discussion on cutting meshes.
result Detailed understanding and definitions of polygonal mesh topology, including intrinsic and extrinsic properties.
HyperNOMAD automates deep neural network hyperparameter tuning.
problem Automating the calibration of hyperparameters in deep neural networks.
method Derivative-free optimization using MADS algorithm.
result Achieves comparable results to state-of-the-art methods.
DISTANA predicts and denoises spatial wave dynamics.
problem Identifying causality in spatially distributed, non-linear dynamical processes.
method Generative, recurrent graph convolution neural network architecture (DISTANA).
result DISTANA outperforms alternative approaches in denoising and predicting complex spatial wave propagation.
AQFC method estimates mesh curvatures using quadratic surfaces.
problem Estimating curvatures for irregular polygonal meshes.
method Local approximation of vertices and normals by quadratic surfaces, computed as implicit surfaces.
result AQFC provides robust curvature estimation for irregular meshes.