Publications

19 Results
Skip to search filters

MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources

Computational Mechanics

Gorodetsky, Alex A.; Jakeman, J.D.; Geraci, G.

We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data—we can combine noisy, non-nested evaluations of the information sources. Numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.

More Details
TYPE Journal Article YEAR 2021
ScopusOSTIDOI

Low-rank tensor integration for Gaussian filtering of continuous time nonlinear systems

2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017

Gorodetsky, Alex A.; Karaman, Sertac; Marzouk, Youssef M.

Integration-based Gaussian filters such as un-scented, cubature, and Gauss-Hermite filters are effective ways to assimilate data and models within nonlinear systems. Traditionally, these filters have only been applicable for systems with a handful of states due to stability and scalability issues. In this paper, we present a new integration method for scaling quadrature-based filters to higher dimensions. Our approach begins by decomposing the dynamics and observation models into separated, low-rank tensor formats. Once in low-rank tensor format, adaptive integration techniques may be used to efficiently propagate the mean and covariance of the distribution of the system state with computational complexity that is polynomial in dimension and rank. Simulation results are shown on nonlinear chaotic systems with 20 state variables.

More Details
TYPE Conference Poster YEAR 2018
ScopusOSTIDOI
19 Results
19 Results