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Fluid flow around a random distribution of stationary spherical particles is a problem of substantial importance in the study of dispersed multiphase flows. In this paper we present a machine learning methodology using Generative…
Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. A simple and interpretable way to learn a dynamical system from data is to interpolate…
This text describes a method to simultaneously reconstruct flow states and determine particle properties from Lagrangian particle tracking (LPT) data. LPT is a popular measurement strategy for fluids in which particles in a flow are…
We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution,…
The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…
We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
A theoretically interesting and practically important question in cosmology is the reconstruction of the initial density distribution provided a late-time density field. This is a long-standing question with a revived interest recently,…
We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…
Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…
The explicit semi-Lagrangian method method for solution of Lagrangian transport equations as developed in [Natarajan and Jacobs, Computer and Fluids, 2020] is adopted for the solution of stochastic differential equations that is consistent…
This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous.…
Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…
Spherical deconvolution is a widely used approach to quantify fiber orientation distribution from diffusion MRI data. The damped Richardson-Lucy (dRL) is developed to perform robust spherical deconvolution on single shell diffusion MRI…
We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…
Accurately reconstructing continuous flow fields from sparse or indirect measurements remains an open challenge, as existing techniques often suffer from oversmoothing artifacts, reliance on heterogeneous architectures, and the…
We propose a novel Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation…
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…