Related papers: Double Diffusion Maps and their Latent Harmonics f…

Analyzing signals arising from dynamical systems typically requires many modeling assumptions and parameter estimation. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality". In this paper, we…

As deep learning models grow in complexity and the volume of training data increases, reducing storage and computational costs becomes increasingly important. Dataset distillation addresses this challenge by synthesizing a compact set of…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

As synthetic data proliferates across the Internet, it is often reused to train successive generations of generative models. This creates a ``self-consuming loop" that can lead to training instability or \textit{model collapse}. Common…

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…

We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…

While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Finding appropriate low dimensional representations of high-dimensional multi-modal data can be challenging, since each modality embodies unique deformations and interferences. In this paper, we address the problem using manifold learning,…

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…

Diffusion models (DMs) excel in photo-realistic image synthesis, but their adaptation to LiDAR scene generation poses a substantial hurdle. This is primarily because DMs operating in the point space struggle to preserve the curve-like…

In this study we develop dimension-reduction techniques to accelerate diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models (hence, CSDM): First, compress…

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

Diffusion models are a powerful class of generative models capable of producing high-quality images from pure noise using a simple text prompt. While most methods which introduce additional spatial constraints into the generated images…

Flood prediction is critical for emergency planning and response to mitigate human and economic losses. Traditional physics-based hydrodynamic models generate high-resolution flood maps using numerical methods requiring fine-grid…

Humans are skillful navigators: We aptly maneuver through new places, realize when we are back at a location we have seen before, and can even conceive of shortcuts that go through parts of our environments we have never visited. Current…

The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…

Many reinforcement learning (RL) tasks provide the agent with high-dimensional observations that can be simplified into low-dimensional continuous states. To formalize this process, we introduce the concept of a DeepMDP, a parameterized…