Related papers: Physics-Enforced Neural Ordinary Differential Equa…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
Galaxy formation and evolution critically depend on understanding the complex photo-chemical processes that govern the evolution and thermodynamics of the InterStellar Medium (ISM). Computationally, solving chemistry is among the most heavy…
In this work we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large--scale systems of quadratic autonomous Ordinary Differential Equations (ODEs) modeling, e.g., the…
Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…
From neural ODEs to continuous-time machine learning, differentiable solvers allow physics, optimization, and simulation to become trainable components within deep learning systems. This has opened the path to a new generation of deep…
Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…
Diffusion models have recently emerged as a potent tool in generative modeling. However, their inherent iterative nature often results in sluggish image generation due to the requirement for multiple model evaluations. Recent progress has…
Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs and physics informed variants often require orders of…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables,…
Forecasting over graph-structured sensor networks demands models that capture both deterministic spatial trends and stochastic variability, while remaining efficient enough for repeated inference as new observations arrive. We propose…
We present PIVONet (Physically-Informed Variational ODE Neural Network), a unified framework that integrates Neural Ordinary Differential Equations (Neuro-ODEs) with Continuous Normalizing Flows (CNFs) for stochastic fluid simulation and…
Traditionally, calcium dynamics in neurons are modeled using partial differential equations (PDEs) and ordinary differential equations (ODEs). The PDE component focuses on reaction-diffusion processes, while the ODE component addresses…
Efficient chemical kinetic model inference and application in combustion are challenging due to large ODE systems and widely separated time scales. Machine learning techniques have been proposed to streamline these models, though strong…
Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other. These networks consist of a feature extractor, a correlation volume, and finally several…
In this work, we focus on the alignment problem of diffusion models with a continuous reward function, which represents specific objectives for downstream tasks, such as increasing darkness or improving the aesthetics of images. The central…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…
Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…
Neural Ordinary Differential Equations (Neural ODEs) construct the continuous dynamics of hidden units using ordinary differential equations specified by a neural network, demonstrating promising results on many tasks. However, Neural ODEs…
The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…