Related papers: Joint Parameter Discovery and Generative Modeling …

Car-following behavior modeling is critical for understanding traffic flow dynamics and developing high-fidelity microscopic simulation models. Most existing impulse-response car-following models prioritize computational efficiency and…

Identifying the physical properties of the surrounding environment is essential for robotic locomotion and navigation to deal with non-geometric hazards, such as slippery and deformable terrains. It would be of great benefit for robots to…

All physical laws are described as relationships between state variables that give a complete and non-redundant description of the relevant system dynamics. However, despite the prevalence of computing power and AI, the process of…

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…

Musculoskeletal models have been widely used for detailed biomechanical analysis to characterise various functional impairments given their ability to estimate movement variables (i.e., muscle forces and joint moment) which cannot be…

We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics. By lifting neural parameters to a measure space and modeling training as Wasserstein…

Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for…

We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we…

Dynamic patterns are characterized by complex spatial and motion patterns. Understanding dynamic patterns requires a disentangled representational model that separates the factorial components. A commonly used model for dynamic patterns is…

This paper presents a machine learning framework (GP-NODE) for Bayesian systems identification from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in…

We study the tracking problem, namely, estimating the hidden state of an object over time, from unreliable and noisy measurements. The standard framework for the tracking problem is the generative framework, which is the basis of solutions…

Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…

Modeling biological rhythms helps understand the complex principles behind the physical and psychological abnormalities of human bodies, to plan life schedules, and avoid persisting fatigue and mood and sleep alterations due to the…

Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…

Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal…

Identifying the intrinsic coordinates or modes of the dynamical systems is essential to understand, analyze, and characterize the underlying dynamical behaviors of complex systems. For nonlinear dynamical systems, this presents a critical…

We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…