相关论文: Discovering governing equation in structural dynam…

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…

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…

Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon…

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…

Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

We show a data-driven approach to discover the underlying structural form of the mathematical equation governing the dynamics of multiple but similar systems induced by the same mechanisms. This approach hinges on theories that we lay out…

Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states. To learn the laws of systems, all previous methods for equation discovery in hybrid systems follow a two-stage…

Understanding how systems evolve over time often requires discovering the differential equations that govern their behavior. Automatically learning these equations from experimental data is challenging when the data are noisy or limited,…

Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…

The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited great success to learn and predict dynamical systems from…

Certain neural network architectures, in the infinite-layer limit, lead to systems of nonlinear differential equations. Motivated by this idea, we develop a framework for analyzing time signals based on non-autonomous dynamical equations.…

Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…

Approximate Bayesian Computation (ABC) methods have gained in their popularity over the last decade because they expand the horizon of Bayesian parameter inference methods to the range of models for which only forward simulation is…

The value of unknown parameters of multibody systems is crucial for prediction, monitoring, and control, sometimes estimated using a biased physics-based model leading to incorrect outcomes. Discovering motion equations of multibody systems…

This paper presents the use of spike-and-slab (SS) priors for discovering governing differential equations of motion of nonlinear structural dynamic systems. The problem of discovering governing equations is cast as that of selecting…

We propose a robust parameter estimation method for dynamical systems based on Statistical Learning techniques which aims to estimate a set of parameters that well fit the dynamics in order to obtain robust evidences about the qualitative…

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…