arXiv subjects

Juan A. Saenz

Publications and source records attributed to Juan A. Saenz.

3 recordsLinked to original sources

arXiv2021

Objective discovery of dominant dynamical processes with intelligible machine learning

The advent of big data has vast potential for discovery in natural phenomena ranging from climate science to medicine, but overwhelming complexity stymies insight. Existing theory is often not able to succinctly describe salient phenomena, and progress has largely relied on ad hoc definitions of dynamical regimes to guide and focus exploration. We present a formal definition in which the identification of dynamical regimes is formulated as an optimization problem, and we propose an intelligible objective function. Furthermore, we propose an unsupervised learning framework which eliminates the need for a priori knowledge and ad hoc definitions; instead, the user need only choose appropriate clustering and dimensionality reduction algorithms, and this choice can be guided using our proposed objective function. We illustrate its applicability with example problems drawn from ocean dynamics, tumor angiogenesis, and turbulent boundary layers. Our method is a step towards unbiased data exploration that allows serendipitous discovery within dynamical systems, with the potential to propel the physical sciences forward.

cs.LG↗

arXiv2020

Interpreting neural network models of residual scalar flux

We show that in addition to providing effective and competitive closures, when analysed in terms of dynamics and physically-relevant diagnostics, artificial neural networks (ANNs) can be both interpretable and provide useful insights in the on-going task of developing and improving turbulence closures. In the context of large-eddy simulations (LES) of a passive scalar in homogeneous isotropic turbulence, exact subfilter fluxes obtained by filtering direct numerical simulations (DNS) are used both to train deep ANN models as a function of filtered variables, and to optimise the coefficients of a turbulent Prandtl number LES closure. \textit{A-priori} analysis of the subfilter scalar variance transfer rate demonstrates that learnt ANN models out-perform optimised turbulent Prandtl number closures and Clark-type gradient models. Next, \textit{a-posteriori} solutions are obtained with each model over several integral timescales. These experiments reveal, with single- and multi-point diagnostics, that ANN models temporally track exact resolved scalar variance with greater accuracy compared to other subfilter flux models for a given filter length scale. Finally, we interpret the artificial neural networks statistically with differential sensitivity analysis to show that the ANN models feature dynamics reminiscent of so-called "mixed models", where mixed models are understood as comprising both a structural and functional component. Besides enabling enhanced-accuracy LES of passive scalars henceforth, we anticipate this work to contribute to utilising neural network models as a tool in interpretability, robustness and model discovery.

physics.comp-ph↗

arXiv2019

Turbulence forecasting via Neural ODE

Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational demands associated with explicitly resolving the full set of scales and their interactions, as in the Direct Numerical Simulation (DNS) of the Navier-Stokes equations, in most problems of practical interest are so high that reduced modeling of scales and interactions is required before further progress can be made. While popular reduced models are typically based on phenomenological modeling of relevant turbulent processes, recent advances in machine learning techniques have energized efforts to further improve the accuracy of such reduced models. In contrast to such efforts that seek to improve an existing turbulence model, we propose a machine learning(ML) methodology that captures, de novo, underlying turbulence phenomenology without a pre-specified model form. To illustrate the approach, we consider transient modeling of the dissipation of turbulent kinetic energy, a fundamental turbulent process that is central to a wide range of turbulence models using a Neural ODE approach. After presenting details of the methodology, we show that this approach outperforms state-of-the-art approaches.

physics.comp-ph↗