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Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…

Redundant manipulators, with their higher Degrees of Freedom (DoFs), offer enhanced kinematic performance and versatility, making them suitable for applications like manufacturing, surgical robotics, and human-robot collaboration. However,…

Multirotors flying in close proximity induce aerodynamic wake effects on each other through propeller downwash. Conventional methods have fallen short of providing adequate 3D force-based models that can be incorporated into robust control…

Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational…

This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The…

Geographical, physical, or economic constraints often result in missing traces within seismic data, making the reconstruction of complete seismic data a crucial step in seismic data processing. Traditional methods for seismic data…

In many real-world regression tasks, the data distribution is heavily skewed, and models learn predominantly from abundant majority samples while failing to predict minority labels accurately. While imbalanced classification has been…

Generative models have recently undergone significant advancement due to the diffusion models. The success of these models can be often attributed to their use of guidance techniques, such as classifier or classifier-free guidance, which…

Diffusion probabilistic models have achieved enormous success in the field of image generation and manipulation. In this paper, we explore a novel paradigm of using the diffusion model and classifier guidance in the latent semantic space…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

Goal-conditioned planning benefits from learned low-dimensional representations of rich observations. While compact latent representations typically learned from variational autoencoders or inverse dynamics enable goal-conditioned decision…

We introduce a new methodology for forecasting which we call Signal Diffusion Mapping. Our approach accommodates features of real world financial data which have been ignored historically in existing forecasting methodologies. Our method…

Advancements in mobility services, navigation systems, and smart transportation technologies have made it possible to collect large amounts of path data. Modeling the distribution of this path data, known as the Path Generation (PG)…

Large datasets have become commonplace in NLP research. However, the increased emphasis on data quantity has made it challenging to assess the quality of data. We introduce Data Maps---a model-based tool to characterize and diagnose…

We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an…

Multi-arm motion planning is fundamental for enabling arms to complete complex long-horizon tasks in shared spaces efficiently but current methods struggle with scalability due to exponential state-space growth and reliance on large…

We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps are used to approximate the generator of the corresponding…

3D data simulation aims to bridge the gap between simulated and real-captured 3D data, which is a fundamental problem for real-world 3D visual tasks. Most 3D data simulation methods inject predefined physical priors but struggle to capture…

Large-scale foundation models for scientific machine learning adapt to physical settings unseen during training, such as zero-shot transfer between turbulent scales. This phenomenon, in-context learning, challenges conventional…

We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…