Related papers: Engineered Ordinary Differential Equations as Clas…

Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…

We propose NECA, a deep representation learning method for categorical data. Built upon the foundations of network embedding and deep unsupervised representation learning, NECA deeply embeds the intrinsic relationship among attribute values…

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

This paper proposes and studies a detection technique for adversarial scenarios (dubbed deterministic detection). This technique provides an alternative detection methodology in case the usual stochastic methods are not applicable: this can…

In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…

We introduce a new second-order inertial optimization method for machine learning called INNA. It exploits the geometry of the loss function while only requiring stochastic approximations of the function values and the generalized…

Estimation-of-distribution algorithms (EDAs) are general metaheuristics used in optimization that represent a more recent alternative to classical approaches like evolutionary algorithms. In a nutshell, EDAs typically do not directly evolve…

We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…

Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…

In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of dynamic experiments to generate input-output…

Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…