Related papers: Rediscovering shallow water equations from experim…
Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…
The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs) from data poses significant challenges, primarily in…
This paper introduces a novel anomaly detection framework that combines the robust statistical principles of density-estimation-based anomaly detection methods with the representation-learning capabilities of deep learning models. The…
We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schr\"odinger type is coupled to an equation of Korteweg-de Vries type. Such systems model…
Shockwaves provide a useful and rewarding route to the nonequilibrium properties of simple fluids far from equilibrium. For simplicity, we study a strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear transport…
This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…
We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…
We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The model is a version of a conditional variational auto-encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty…
We continue our study on the convergence issue of the intermediate long wave equation (ILW) on both the real line and the circle. In particular, we establish convergence of the scaled ILW dynamics to that of the Korteweg-de Vries equation…
Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…
In this paper we apply the approach of formal asymptotic expansions and perturbation theory to derive a new highly nonlinear shallow-water model from the full governing equations for two dimensional incompressible fluid with constant…
Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models…
We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the…
Discovering the governing equations of evolving systems from available observations is essential and challenging. In this paper, we consider a new scenario: discovering governing equations from streaming data. Current methods struggle to…
Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration.…
We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the…
The extended KdV equation is a nonlinear dispersive wave model that is asymptotically or variationally derived from the full dispersive Euler shallow water waves equations when gravity-capillary and higher order nonlinear effects are taken…
The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…