Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences

Abstract

Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. However, machine learning alone ignores the fundamental laws of physics and can result in ill-posed problems or non-physical solutions. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. However, multiscale modeling alone often fails to efficiently combine large datasets from different sources and different levels of resolution. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We review the current literature, highlight applications and opportunities, address open questions, and discuss potential challenges and limitations in four overarching topical areas: ordinary differential equations, partial differential equations, data-driven approaches, and theory-driven approaches. Towards these goals, we leverage expertise in applied mathematics, computer science, computational biology, biophysics, biomechanics, engineering mechanics, experimentation, and medicine. Our multidisciplinary perspective suggests that integrating machine learning and multiscale modeling can provide new insights into disease mechanisms, help identify new targets and treatment strategies, and inform decision making for the benefit of human health.

Keywords: Computational biophysics; Computational science.

Fig. 1. Machine learning and multiscale modeling in the biological, biomedical, and behavioral sciences.

Machine learning and multiscale modeling interact on the parameter level via constraining parameter spaces, identifying parameter values, and analyzing sensitivity and on the system level via exploiting the underlying physics, constraining design spaces, and identifying system dynamics. Machine learning provides the appropriate tools towards supplementing training data, preventing overfitting, managing ill-posed problems, creating surrogate models, and quantifying uncertainty with the ultimate goal being to explore massive design spaces and identify correlations. Multiscale modeling integrates the underlying physics towards identifying relevant features, exploring their interaction, elucidating mechanisms, bridging scales, and understanding the emergence of function with the ultimate goal of predicting system dynamics and identifying causality.

Fig. 2. Machine learning and multiscale modeling of the cardiac system.

Multiscale modeling can teach machine learning how to exploit the underlying physics described by, e.g., the ordinary differential equations of cellular electrophysiology and the partial differential equations of electro-mechanical coupling, and constrain the design spaces; machine learning can teach multiscale modeling how to identify parameter values, e.g., the gating variables that govern local ion channel dynamics, and identify system dynamics, e.g., the anisotropic signal propagation that governs global diffusion. This natural synergy presents new challenges and opportunities in the biological, biomedical, and behavioral sciences.

Fig. 3. Partial differential equations encode physics-based knowledge into machine learning.

Physics imposed on neural networks. The neural network on the left, as yet unconstrained by physics, represents the solution u(x, t) of the partial differential equation; the neural network on the right describes the residual f(x, t) of the partial differential equation. The example illustrates a one-dimensional version of the Schrödinger equation with unknown parameters λ₁ and λ₂ to be learned. In addition to unknown parameters, we can learn missing functional terms in the partial differential equation. Currently, this optimization is done empirically based on trial and error by a human-in-the-loop. Here, the u-architecture is a fully connected neural network, while the f-architecture is dictated by the partial differential equation and is, in general, not possible to visualize explicitly. Its depth is proportional to the highest derivative in the partial differential equation times the depth of the uninformed neural network.

Fig. 4. Data-driven machine learning seeks correlations in big data.

This general framework integrates data-driven multiscale modeling and machine learning by performing organ, cellular, or molecular level simulations and systematically comparing the simulation results against experimental target data using machine learning analysis including clustering, regression, dimensionality reduction, reinforcement learning, and deep learning with the objectives to identify parameters, generate new hypotheses, or optimize treatment.

Fig. 5. Theory-driven machine learning seeks causality by integrates prior knowledge and big data.

Accelerating model- and data-driven discovery by integrating theory-driven machine learning and multiscale modeling. Theory-driven machine learning can yield data-efficient workflows for predictive modeling by synthesizing prior knowledge and multimodality data at different scales. Probabilistic formulations can also enable the quantification of predictive uncertainty and guide the judicious acquisition of new data in a dynamic model-refinement setting.