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Spatiotemporal trajectory data is crucial for various applications. However, issues such as device malfunctions and network instability often cause sparse trajectories, leading to lost detailed movement information. Recovering the missing…

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor…

Multi-agent trajectory prediction is crucial for various practical applications, spurring the construction of many large-scale trajectory datasets, including vehicles and pedestrians. However, discrepancies exist among datasets due to…

Pedestrian trajectory prediction in a first-person view has recently attracted much attention due to its importance in autonomous driving. Recent work utilizes pedestrian character information, \textit{i.e.}, action and appearance, to…

An important problem in the analysis of high-dimensional omics data is to identify subsets of molecular variables that are associated with a phenotype of interest. This requires addressing the challenges of high dimensionality, strong…

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional…

Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…

We introduce the Discrete Inverse Continuity Equation (DICE) method, a generative modeling approach that learns the evolution of a stochastic process from given sample populations at a finite number of time points. Models learned with DICE…

Target tracking plays a crucial role in real-world scenarios, particularly in drug-trafficking interdiction, where the knowledge of an adversarial target's location is often limited. Improving autonomous tracking systems will enable…

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of…

The multi-modality and stochastic characteristics of human behavior make motion prediction a highly challenging task, which is critical for autonomous driving. While deep learning approaches have demonstrated their great potential in this…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…

We define the object detection from imagery problem as estimating a very large but extremely sparse bounding box dependent probability distribution. Subsequently we identify a sparse distribution estimation scheme, Directed Sparse Sampling,…

Continuous dynamical systems are cornerstones of many scientific and engineering disciplines. While machine learning offers powerful tools to model these systems from trajectory data, challenges arise when these trajectories are captured as…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Complex systems in physics, chemistry, and biology that evolve over time with inherent randomness are typically described by stochastic differential equations (SDEs). A fundamental challenge in science and engineering is to determine the…

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

Predicting the dynamics of complex systems is crucial for various scientific and engineering applications. The accuracy of predictions depends on the model's ability to capture the intrinsic dynamics. While existing methods capture key…