Related papers: The data-driven physical-based equations discovery…
Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…
Finding the governing equations from data by sparse optimization has become a popular approach to deterministic modeling of dynamical systems. Considering the physical situations where the data can be imperfect due to disturbances and…
Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
We present a method of discovering governing differential equations from data without the need to specify a priori the terms to appear in the equation. The input to our method is a dataset (or ensemble of datasets) corresponding to a…
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…
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…
In this work we present a data-driven method for the discovery of parametric partial differential equations (PDEs), thus allowing one to disambiguate between the underlying evolution equations and their parametric dependencies. Group…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…
PDE discovery shows promise for uncovering predictive models of complex physical systems but has difficulty when measurements are sparse and noisy. We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully…
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…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…