Comparing Methods for Estimating Marginal Likelihood in Symbolic Regression
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Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.
This is the seminar I will present at WCCM conference highlighting our latest research work on incorporating genetic programming to obtain data-driven strength models for complex materials.
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Computer programs to simulate and translate chosen computer design in Chu computer design language into Boolean equations
Computer oriented error analysis of electrical circuits and nonlinear system performance
Algorithm for Navier-Stokes and continuity equations used to derive curvilinear coordinate system
Network synthesis technique applied to structural dynamics design, using topological formulas to express systems response transfer functions
Digital computer generation of system stability Liapunov functions for ninth order spacecraft attitude control
Writing programs in interactive FORMAC language to implement Picard iteration in solving systems of ordinary differential equations
Using FORMAC system to solve optimal control problem of behavior of higher space derivatives of optimal value function along optimal trajectory
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Data processing to develop a third-order phase model and to translate all such processed data to the frequency realm for further analysis was described. The frequency study yields a long frequency modulation (FM) drift sinusoid (1600-sec period), an impressed secondary drift wave with a period of about 116 sec, and a set of even harmonics of twice the ramp period-the latter arising from, and used to modify, the phase detector model. The result is applied secondarily to estimate the strong-signal SSA phase detector response "out-of-lock." Finally, the main drift components are verified against all available data, and the result is used to estimate minimum lock conditions and the SSA drift effect under normal operating modes. The instability problem appears marginally resolvable if the acquisition technique is modified.