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Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for…

Graph Neural Networks (GNNs) often struggle with noisy edges. We propose Latent Space Constrained Graph Neural Networks (LSC-GNN) to incorporate external "clean" links and guide embeddings of a noisy target graph. We train two encoders--one…

Deep neural networks (DNNs) are known to be vulnerable to adversarial geometric transformation. This paper aims to verify the robustness of large-scale DNNs against the combination of multiple geometric transformations with a provable…

By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…

This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being…

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the…

This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…

The goal of generative models is to learn the intricate relations between the data to create new simulated data, but current approaches fail in very high dimensions. When the true data generating process is based on physical processes these…

Recent work has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of unknown chaotic dynamical systems. Short-term predictions of the state evolution and long-term predictions of the statistical…

Chaotic dynamical systems pose a fundamental challenge for Reinforcement Learning (RL): exponential sensitivity to initial conditions induces high-variance bootstrap targets and poorly conditioned gradient updates. Chaotic dynamics arise…

Deep neural networks (DNN) are increasingly being used to learn controllers due to their excellent approximation capabilities. However, their black-box nature poses significant challenges to closed-loop stability guarantees and performance…

Multi-view learning has progressed rapidly in recent years. Although many previous studies assume that each instance appears in all views, it is common in real-world applications for instances to be missing from some views, resulting in…

While Graph Neural Networks (GNNs) excel on graph-structured data, their performance is fundamentally limited by the quality of the observed graph, which often contains noise, missing links, or structural properties misaligned with GNNs'…

Graph Neural Networks (GNNs) play a pivotal role in graph-based tasks for their proficiency in representation learning. Among the various GNN methods, spectral GNNs employing polynomial filters have shown promising performance on tasks…

The understanding of the dynamics of the velocity gradients in turbulent flows is critical to understanding various non-linear turbulent processes. The pressure-Hessian and the viscous-Laplacian govern the evolution of the…

Reconstructing high-quality 3D meshes and visuals from 3D Gaussian Splatting(3DGS) still remains a central challenge in computer graphics. Although existing models such as SuGaR offer effective solutions for rendering, there is is still…

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic…

We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…

Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties…