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Time-delay mappings constructed using neural networks have proven successful in performing nonlinear system identification; however, because of their discrete nature, their use in bifurcation analysis of continuous-time systems is limited.…
Dynamical systems can autonomously adapt their organization so that the required target dynamics is reproduced. In the previous Rapid Communication [Phys. Rev. E 90,030901(R) (2014)], it was shown how such systems can be designed using…
A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large…
Adversarial imitation learning has become a widely used imitation learning framework. The discriminator is often trained by taking expert demonstrations and policy trajectories as examples respectively from two categories (positive vs.…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
Recent works have demonstrated that the sample complexity of gradient-based learning of single index models, i.e. functions that depend on a 1-dimensional projection of the input data, is governed by their information exponent. However,…
How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
As autonomous systems become more complex and integral in our society, the need to accurately model and safely control these systems has increased significantly. In the past decade, there has been tremendous success in using deep learning…
Along with the practical success of the discovery of dynamics using deep learning, the theoretical analysis of this approach has attracted increasing attention. Prior works have established the grid error estimation with auxiliary…
Developing and fielding complex systems requires proof that they are reliably correct with respect to their design and operating requirements. Especially for autonomous systems which exhibit unanticipated emergent behavior, fully…
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…
We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed.…
The learning dynamics of on-line independent component analysis is analysed in the limit of large data dimension. We study a simple Hebbian learning algorithm that can be used to separate out a small number of non-Gaussian components from a…
We present a method for efficient differentiable simulation of articulated bodies. This enables integration of articulated body dynamics into deep learning frameworks, and gradient-based optimization of neural networks that operate on…
We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…
Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…
System identification aims to build models of dynamical systems from data. Traditionally, choosing the model requires the designer to balance between two goals of conflicting nature; the model must be rich enough to capture the system…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…