Related papers: Two-Parameter Flows for Learning Population Dynami…
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or…
Even though the analysis of unsteady 2D flow fields is challenging, fluid mechanics experts generally have an intuition on where in the simulation domain specific features are expected. Using this intuition, showing similar regions enables…
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…
Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture…
Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each…
We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate…
A two parameter model for single lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. Despite its simplicity, this model exhibits a rich phenomenology, analogous to that observed in real traffic,…
The stochastics two-layer quasi-geostrophic flow model is an intermediate system between the single-layer two dimensional barotropic flow model and the continuously stratified three dimensional baroclinic flow model. This model is widely…
Scientific data, from cellular snapshots in biology to celestial distributions in cosmology, often consists of static patterns from underlying dynamical systems. These snapshots, while lacking temporal ordering, implicitly encode the…
This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly…
Reduced-order modelling and system identification can help us figure out the elementary degrees of freedom and the underlying mechanisms from the high-dimensional and nonlinear dynamics of fluid flow. Machine learning has brought new…
Drawing inspiration from the lateral lines of fish, the inference of flow characteristics via surface-based data has drawn considerable attention. The current approaches often rely on analytical methods tailored exclusively for potential…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
A data-driven methodology is proposed to model the distribution of multivariate stochastic trajectories from an observed sample. As a first step, each trajectory in the sample is reduced to a vector of features by means of Functional…
Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
Simulating trajectories of dynamical systems is a fundamental problem in a wide range of fields such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based…
Conditional Normalizing Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and large interdimensional correlations, making them appealing for structured output learning.…