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We propose L3DG, the first approach for generative 3D modeling of 3D Gaussians through a latent 3D Gaussian diffusion formulation. This enables effective generative 3D modeling, scaling to generation of entire room-scale scenes which can be…
Established theoretical studies of diffusion in rugged (or rough) potential surfaces have largely focused on quenched energy landscapes. Here we study diffusion on a rugged energy landscape in the presence of dynamic disorder, a situation…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
DC networks play an important role within the ongoing energy transition. In this context, simulations of designed and existing networks and their corresponding assets are a core tool to get insights and form a support to decision-making.…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…
This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…
Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient $(D)$ of a Brownian particle on the distribution width $(\varepsilon)$ of…
This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
We present a structure-preserving Eulerian algorithm for solving $L^2$-gradient flows and a structure-preserving Lagrangian algorithm for solving generalized diffusions. Both algorithms employ neural networks as tools for spatial…
The emergence of organized multiscale patterns resulting from convection is ubiquitous, observed throughout different cloud types. The reproduction of such patterns by general circulation models remains a challenge due to the complex nature…
Turbulence governs the transport of momentum, energy, and scalars in many geophysical and engineering flows. In large-eddy simulations (LES), parameterizing subgrid-scale (SGS) stresses remains a central challenge, as unresolved physical…
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…
How do landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static.…
Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underlying noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…
Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to…
Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are…