Related papers: Machine Learning Conservation Laws of Dynamical sy…
Learning rules -- prescriptions for updating model parameters to improve performance -- are typically assumed rather than derived. Why do some learning rules work better than others, and under what assumptions can a given rule be considered…
Recent advances in learning or identification of nonlinear dynamics focus on learning a suitable model within a pre-specified model class. However, a key difficulty that remains is the choice of the model class from which the dynamics will…
We present a machine-learning scheme based on the relativistic dynamics of a quantum system, namely a quantum detector inside a cavity resonator. An equivalent analog model can be realized for example in a circuit QED platform subject to…
We describe a methodology to build vectorial kinetic schemes, targetting the numerical solution of linear symmetric-hyperbolic systems of conservation laws -a minimal application case for those schemes. Precisely, we fully detail the…
We describe a machine learning method for predicting the value of a real-valued function, given the values of multiple input variables. The method induces solutions from samples in the form of ordered disjunctive normal form (DNF) decision…
The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…
We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods…
We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
Nonlinear string vibration, in particular the case of nonplanar motion, has been an area of intense study for many years. Numerical simulation methods, essential for the comparison between measured data and theory, have received somewhat…
Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…
Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency, and subjective human factors. We developed a novel data-driven geological feature detection…
We introduce and test a general machine-learning-based technique for the inference of short term causal dependence between state variables of an unknown dynamical system from time series measurements of its state variables. Our technique…
Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-reduced models of nonlinear conservation laws which are…
We describe a machine-learning system that uses linear vector-space based techniques for inference from observations to extend previous work on model construction for particle physics (Valdes-Perez 96, 94, Kocabas 91). The program searches…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conservation law. All conservation laws belong to the kernel of…
We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic…