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Integrating Machine Learning and Multiscale Modeling: Perspectives, Challenges, and Opportunities in the Biological, Biomedical, and Behavioral Sciences
Mark Alber, Adrian Buganza Tepole, William Cannon, Suvranu De, Salvador Dura-Bernal, Krishna Garikipati, George Karniadakis, William W. Lytton, Paris Perdikaris, Linda Petzold, Ellen Kuhl
TL;DR
Biological, biomedical, and behavioral sciences need efficient ways to interpret massive, multimodal data, but machine learning can ignore physics while multiscale modeling struggles to combine heterogeneous data. The paper reviews how integrating both approaches can build physics-consistent predictive models for ill-posed problems and large design spaces. It identifies robust sparse-data modeling, ill-posed inference, and efficient design-space exploration as major challenges and opportunities.
Problem
The field lacks efficient strategies that simultaneously handle massive heterogeneous data, incomplete observations, and incompletely understood governing physics.
Method
The paper critically reviews data-driven and theory-driven integrations of machine learning with multiscale modeling, including physics-based constraints, multifidelity data, uncertainty quantification, and data acquisition.
Results
The review concludes that machine learning and multiscale modeling mutually complement one another for correlation discovery, causal analysis, uncertainty quantification, and robust predictive modeling.
Takeaways & Limitations
The integration offers a framework for robust mechanistic models, ill-posed biological inference, and efficient exploration of massive biomedical design spaces.
Takeaways & Limitations
Physics-informed predictions can remain difficult to assess when the model’s functional form is not explicit, making it unclear whether results are correct for the right reasons.
Abstract
from arXiv · showhide
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, classical machine learning techniques often ignore the fundamental laws of physics and 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 data sets from different sources and different levels of resolution. We show how machine learning and multiscale modeling can complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We critically 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.
MOTIVATION
Biological systems are difficult to model because living matter adapts dynamically and involves interacting biological, chemical, mechanical, and electrical fields. Machine learning and multiscale modeling therefore complement one another by combining data integration with physics-based mechanisms, uncertainty analysis, and system-level understanding.
- MOTIVATION: Living matter adapts to its environment, generates force, contracts, rearranges its architecture, and changes size, requiring expanded physical modeling.Appropriate models may need revised kinetics, mass balance, and thermodynamic laws, together with biological, chemical, or electrical stimuli.
- MOTIVATION: Multiscale modeling contributes underlying physics, relevant features, cross-scale interactions, mechanisms, and explanations of emergent function.Its system-level goal is to predict dynamics and identify causality.
- MOTIVATION: Machine learning preprocesses massive data, integrates modalities and fidelities, identifies correlations, and infers overall system dynamics.It can also compare simulated and experimentally measured features across scales using Bayesian inference and uncertainty quantification.
- MOTIVATION: The two approaches complement one another: machine learning reveals correlations and quantifies uncertainty, while multiscale modeling probes causality and identifies mechanisms.This integration can incorporate partial differential equations, boundary conditions, and physical constraints such as conservation, symmetry, and invariance.
- MOTIVATION: Their integration operates at parameter and system levels by constraining parameter and design spaces, identifying parameter values and dynamics, and analyzing sensitivity.Machine learning also supports training-data supplementation, overfitting prevention, surrogate modeling, and ill-posed-problem management.
CHALLENGES
The central challenge is to understand biological systems when data are incomplete and governing physics and parameters are uncertain. The paper presents machine-learning approaches that incorporate physical knowledge, combine data across fidelities, and support robust inference and prediction.
- CHALLENGES: Incomplete data and incompletely known governing equations make biological-system understanding a central modeling challenge.The ideal conditions—complete high-resolution data or validated physics equations and parameters—are generally unavailable.
- CHALLENGES: Multi-fidelity modeling combines abundant, inexpensive low-fidelity data with sparse, expensive high-fidelity data to create efficient and robust surrogate models.Examples include mixed-convection flow past a cylinder and cardiac electrophysiology.
- CHALLENGES: Physics-informed neural networks solve supervised learning tasks while respecting physical constraints, including applications to cardiovascular diagnosis and intracranial aneurysm flow surrogates.These models connect predictive learning with governing physical principles.
- CHALLENGES: Partial differential equations, boundary conditions, and constraints can regularize machine learning to learn robustly from small, noisy data evolving across space and time.Gaussian processes and neural networks are particularly powerful for encoding this prior physics-based information.
- CHALLENGES: Theory-driven approaches can guide informative data acquisition, explore massive design spaces, and construct predictive models that obey conservation, symmetry, or invariance.Examples include recovering constitutive laws from mesoscopic simulations and modeling cell metabolism using reaction-conservation laws with unknown rate functions.
OPEN QUESTIONS AND OPPORTUNITIES
The paper identifies open questions for combining machine learning with multiscale modeling, spanning ill-posed problems, missing information, surrogate models, discretization, training data, uncertainty, mechanisms, and biologically inspired learning. It also highlights limitations involving overfitting, data bias, validation, and reproducibility.
- Managing ill-posed problems: Ill-posed inverse problems in biological systems require methods that address unknown boundary values and associated uncertainty.
- Identifying missing information: Multiscale simulations and generative networks could run alongside experiments to independently assess parameter sensitivity and identify missing information.
- Creating surrogate models: Generative adversarial networks could create test data for multiscale models, while multiscale simulations could supply training instances for faster surrogate models.
- Discretizing space and time: Automating mesh generation, meshless interpolation, and domain parameterization could reduce the labor required to discretize complex, moving three-dimensional domains.
- Supplementing training data: Simulations across broad parameter ranges can supplement insufficient experimental or clinical data and support physics-informed machine learning.
- Theory-driven and biologically inspired opportunities: Key opportunities include uncertainty quantification, compact representations for massive design spaces, interpretable mechanistic models, and biologically inspired learning architectures.
CONCLUSIONS
The paper identifies five challenges for integrating machine learning with multiscale modeling: sparse data, ill-posed problems, massive design spaces, causal prediction, and methodological limitations. It proposes combining complementary strengths while improving information gain, computational efficiency, mechanistic understanding, and rigor.
- Challenge 4: Causal prediction: Integrating machine learning with multiscale modeling aims to use correlations to explore design spaces and physics-based dynamics to identify causality.The paper frames robust system-dynamics prediction as the driving force behind the integration.
- Challenge 1: Sparse data: Sparse data require identifying missing information, acquiring targeted experiments, and combining low- and high-resolution data across sources.This creates a multifidelity, multimodality strategy aimed at maximizing information gain and efficiency.
- Challenge 2: Ill-posed problems: Physics-informed and hybrid deterministic-stochastic models can constrain ill-posed inverse problems involving parameters or system dynamics.The proposed combinations include classical balance laws, stochastic living-system equations, and physics-informed neural networks.
- Challenge 3: Massive design spaces: Multiscale modeling bridges spatial and temporal scales, while machine learning reduces parameter spaces into surrogate models for efficient exploration of massive design spaces.Real-time big-data analytics is presented as a demanding step toward clinical artificial-intelligence solutions.
- Challenge 5: Limitations: Predictive models remain limited by overfitting, non-physical predictions, data bias, and dependence on the quality of underlying models and training data.The paper emphasizes sensitivity analysis, uncertainty quantification, rigor, and reproducibility as continuing requirements.