Multiscale modeling meets machine learning: What can we learn? PMC

There is, therefore, a pressing need to develop robust inverse methods that are capable of handling sparse data. One example is robust system identification, the creation of mathematical models of dynamical systems from measured experimental data. This naturally implies the optimal design of experiments to efficiently generate informative training data and iterative model refinement or progressive model reduction. System identification refers to a collection of statistical methods that identify the governing equations of a system from data.

Theory-driven approaches

Neural networks can be directly trained against labels for a quantity of interest such as the time-averaged solution or its frequency distribution. Principal component analysis can be applied to the dynamics to develop reduced order models. Deep neural networks can be combined into an approach of multi-fidelity learning 55 that integrates well with multiscale modeling methods. Coarse scale, but plentiful data, for example obtained from larger numbers of trajectories reported at fewer time instants, are used to train low-fidelity neural Web development networks, which are typically shallow and narrow. Progressively finer scale data at increasing numbers of time instants, but for fewer trajectories and expensive to obtain, are used to train higher fidelity deep neural networks to minimize the error between the labels and the output of the low-fidelity neural network.

Data-driven machine learning seeks correlations in big data

Neural differential equations are machine learning models that aim to identify latent dynamic processes from noisy and irregularly sampled time-series data 21. Leveraging recent advances in automatic differentiation 9, they can efficiently back-propagate through ordinary or partial differential equation solvers to calibrate complex dynamic models and perform forecasting with quantified uncertainty. Examples in biomedicine include predicting in-hospital mortality from irregularly sampled time-series containing measurements from the first 48 hours of a different patient’s admission to the intensive care unit 101.

Multiscale modeling seeks to predict the behavior of biological, biomedical, and behavioral systems

• With applications ranging from marketing to social sciences, MDS continues to be a valuable method for data exploration and interpretation.
• Such tasks are usually based on interpolation in that the input domain is well specified, and we have sufficient data to construct models that can interpolate between the dots.
• A more rigorous approach is to derive the constitutive relation frommicroscopic models, such as atomistic models, by taking thehydrodynamic limit.
• For polymer fluids we are often interested inunderstanding how the conformation of the polymer interacts with theflow.

The homogenization, the identification of the constitutive behavior at macroscale from the detailed behavior of representative units at the microscale, is critical to embed this knowledge into tissue or organ level simulations. Would not it be great to have a virtual replica of ourselves to explore our interaction with the real world in real time? A living, digital representation of ourselves that integrates machine learning and multiscale modeling to continuously learn and dynamically update itself as our environment changes in real life? A virtual mirror of ourselves that allows us to simulate our personal medical history and health condition using data-driven analytical algorithms and theory-driven physical knowledge? Can we leverage our knowledge of machine learning and multiscale modeling in the biological, biomedical, and behavioral sciences Multi-scale analysis to accelerate developments towards a Digital Twin? Do we already have digital organ models that we could integrate into a full Digital Twin?

• Intgaussder functions are like special tools that not only smooth out the data but also help you see how the details change as you zoom in and out.
• The renormalization group method has found applications in a varietyof problems ranging from quantum field theory, to statistical physics,dynamical systems, polymer physics, etc.
• In drug development, for example, we can leverage theory-driven machine learning techniques to integrate information across ten orders of magnitude in space and time towards developing interpretable classifiers that enable us to characterize the potency of pro-arrhythmic drugs 104.
• The chapter concludes with a reflection on the current impasse in the field of ecological economics and the potential role of the Barcelona School of Ecological Economics in moving forward.
• Partly forthis reason, the same approach has been followed in modeling complexfluids, such as polymeric fluids.

These approaches are essentially nonlinear optimization problems that learn the set of coefficients by multiplying combinations of algebraic and rate terms that result in the best fit to the observations. For adequate data, the system identification problem is usually relatively robust and can learn a parsimonious set of coefficients, especially with stepwise regression. Clearly, parsimony is central to identifying the correct set of equations and the easiest strategy to satisfy this requirement is classical or stepwise regression. In the multiscale approach, one uses a variety of models at differentlevels of resolution and complexity to study one system.

• They sometimes originate from physical laws ofdifferent nature, for example, one from continuum mechanics and onefrom molecular dynamics.
• Looking at data from many different levels of detail means the model has to do a lot more work.
• We simply have to input the atomic numbers of all the participating atoms, then we have a complete model which is sufficient for chemistry, much of physics, material science, biology, etc.
• It is still not clear what fusion / analysis techniques are best for various detectors.
• Decide between metric or non-metric MDS based on the nature of your data (quantitative or ordinal).
• The choice of scale allows researchers to uncover unique insights and tailor their analyses to specific research questions.
• Realistically, biological parameters may be measured in various species, in various cell types, at various temperatures, at various ages, and in different in vivo and in vitro preparations.