Lukasz Burzawa1,2, Linlin Li1, Xu Wang1, Adrian Buganza-Tepole1,3, David M Umulis1,4. 1. Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907. 2. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907. 3. School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907. 4. Department of Ag. and Biological Engineering, Purdue University, West Lafayette, IN 47907.
Abstract
PURPOSE OF REVIEW: Partial differential equation (PDE) mathematical models of biological systems and the simulation approaches used to solve them are widely used to test hypotheses and infer regulatory interactions based on optimization of the PDE model against the observed data. In this review, we discuss the ability of powerful machine learning methods to accelerate the parametric screening of biophysical informed- PDE systems. RECENT FINDINGS: A major shortcoming in more broad adaptation of PDE-based models is the high computational complexity required to solve and optimize the models and it requires many simulations to traverse the very high-dimensional parameter spaces during model calibration and inference tasks. For instance, when scaling up to tens of millions of simulations for optimization and sensitivity analysis of the PDE models, compute times quickly extend from months to years for sufficient coverage to solve the problems. For many systems, this brute-force approach is simply not feasible. Recently, neural network metamodels have been shown to be an efficient way to accelerate PDE model calibration and here we look at the benefits and limitations in extending the PDE acceleration methods to improve optimization and sensitivity analysis. SUMMARY: We use an example simulation to quantitatively and qualitatively show how neural network metamodels can be accurate and fast and demonstrate their potential for optimization of complex spatiotemporal problems in biology. We expect these approaches will be broadly applied to speed up scientific research and discovery in biology and other systems that can be described by complex PDE systems.
PURPOSE OF REVIEW: Partial differential equation (PDE) mathematical models of biological systems and the simulation approaches used to solve them are widely used to test hypotheses and infer regulatory interactions based on optimization of the PDE model against the observed data. In this review, we discuss the ability of powerful machine learning methods to accelerate the parametric screening of biophysical informed- PDE systems. RECENT FINDINGS: A major shortcoming in more broad adaptation of PDE-based models is the high computational complexity required to solve and optimize the models and it requires many simulations to traverse the very high-dimensional parameter spaces during model calibration and inference tasks. For instance, when scaling up to tens of millions of simulations for optimization and sensitivity analysis of the PDE models, compute times quickly extend from months to years for sufficient coverage to solve the problems. For many systems, this brute-force approach is simply not feasible. Recently, neural network metamodels have been shown to be an efficient way to accelerate PDE model calibration and here we look at the benefits and limitations in extending the PDE acceleration methods to improve optimization and sensitivity analysis. SUMMARY: We use an example simulation to quantitatively and qualitatively show how neural network metamodels can be accurate and fast and demonstrate their potential for optimization of complex spatiotemporal problems in biology. We expect these approaches will be broadly applied to speed up scientific research and discovery in biology and other systems that can be described by complex PDE systems.
Authors: Mark Alber; Adrian Buganza Tepole; William R Cannon; Suvranu De; Salvador Dura-Bernal; Krishna Garikipati; George Karniadakis; William W Lytton; Paris Perdikaris; Linda Petzold; Ellen Kuhl Journal: NPJ Digit Med Date: 2019-11-25