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Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…

Machine learning has witnessed substantial growth, leading to the development of advanced artificial intelligence models crafted to address a wide range of real-world challenges spanning various domains, such as computer vision, natural…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic…

Recent advances in protein structure prediction, such as AlphaFold, have demonstrated the power of deep neural architectures like the Evoformer for capturing complex spatial and evolutionary constraints on protein conformation. However, the…

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating…

Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the…

A method for the numerical solution of variable order (VO) fractional differential equations (FDE) is presented. The method applies to linear as well as to nonlinear VO-FDEs. The Caputo type VO fractional derivative is employed. First, an…

Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis…

Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This…

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for…

Predicting scene dynamics from visual observations is challenging. Existing methods capture dynamics only within observed boundaries failing to extrapolate far beyond the training sequence. Node-RF (Neural ODE-based NeRF) overcomes this…

Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…

The physical world is governed by the laws of physics, often represented in form of nonlinear partial differential equations (PDEs). Unfortunately, solution of PDEs is non-trivial and often involves significant computational time. With…

Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent…