The low-fidelity neural network resolves the low frequency components of the response, with the progressively higher fidelity deep neural networks representing the higher frequencies. The underlying principle is that the knowledge base of the response is resolved by shallower and narrower neural networks, while the critical, high frequency response is left to the high-fidelity deep neural network. Developing these novel approaches is important to accurately resolve the dynamics of, for example, reaction-diffusion systems of ligands and morphogens that together control patterning in developmental biology. Theory-driven machine learning can enable the seamless synthesis of physics-based models at multiple temporal and spatial scales.
Supplementing training data.
E, “Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics,” J. Urban planners use multiple-scale analysis to design sustainable and resilient cities. Some of these techniques aim to homogenize the properties of the local scale; others attempt to capture nonlinear behavior via curve fitting and progressive damage approaches. Many of the most famous techniques, such as those evaluated in the World Wide Failure Exercises, are related to the analysis of unidirectional composites. The key is that the user must be very aware of the assumptions and bounds of their model when employing one of these techniques. Solving each scale individually and linking their results is much faster than trying to solve a single high-resolution model containing all relevant details.
Quantum mechanics – molecular mechanics (QM-MM) methods
You see the picture in one way, either zoomed out to see the whole scene or zoomed in to see small details. This method can be simpler and faster but might miss important information if the level of detail chosen is not right for the task. A major challenge in theory-driven approaches towards understanding biological, biomedical, and behavioral systems, is obtaining sufficient data to answer the driving question of interest. For example, machine learning could be used to explore responses of both immune and tumor cells in cancer based on single-cell data. A multiscale model could then be built on the families of solutions to codify the evolution of the tumor at organ- or metastasis-scale.
- For example, when modeling the dynamics of a cell, we may know the rate laws that need to be solved and obtain the rate parameters using an optimization algorithm; yet, which reactions are regulated under what conditions may be a mystery for which there are no adequate models.
- Multiscale modeling is a critical step, since biological systems typically possess a hierarchy of structure, mechanical properties, and function across the spatial and temporal scales.
- From a conceptual point of view, this is a problem of supplementing the set of known physics-based equations with constitutive equations, an approach, which has long been used in traditional engineering disciplines.
- If onewants to compute the inter-atomic forces from the first principleinstead of modeling them empirically, then it is much more efficientto do this on-the-fly.
- Ideally, multiscale modeling parameters are all based on consistent experimental measurements.
Why is multi-scale analysis important in machine learning?
Theory-driven machine learning is both a decently mature and quickly evolving area of research. It is mature in that methods for learning parameters for a model such as dynamic programming and variational methods have been known and applied for a long time. Although these methods are generally not considered to be tools of machine learning, the difference between them and current machine learning techniques may be as simple as the difference between a deterministic and a stochastic search 138. Dynamic programing and variational methods are very powerful when we know the form of the model and need to constrain the parameters Multi-scale analysis within a specified range to reproduce experimental observations. Machine learning methods, however, can be very powerful when the model is completely unknown or when there is uncertainty about its form. For example, when modeling the dynamics of a cell, we may know the rate laws that need to be solved and obtain the rate parameters using an optimization algorithm; yet, which reactions are regulated under what conditions may be a mystery for which there are no adequate models.
- Modeling tissue adaptation thus involves accounting for classical equilibrium principles, e.g., momentum and energy, as well as signaling network dynamics often described by stochastic reactive transport models with many variables and parameters.
- This application of machine learning in multiscale modeling is obvious, yet still unaccomplished.
- Non-metric Multidimensional Scaling finds a non-parametric monotonic relationship between dissimilarities and Euclidean distances between items, along with the location of each item in the low-dimensional space.
- For example, composite materials that are used for various products in recent years consist of multiple, various materials.
- Some of these techniques aim to homogenize the properties of the local scale; others attempt to capture nonlinear behavior via curve fitting and progressive damage approaches.
However, deep learning techniques can exploit the compositional Coding structure of approximating functions and can, in principle, beat the curse of dimensionality 87. Generative adversarial networks can also be useful for effective modeling of parameterized partial differential equations with thousands of uncertain parameters 140,141. The most prominent potential application of machine learning in biomechanics is in the determination of response functions including stress-strain relations or cell-scale laws in continuum theories of growth and remodeling 4. These relations take the form of both ordinary differential equations, for which system identification is of relevance, and direct response functions, for which the framework of deep neural networks is applicable 103. For example, a recent study integrated machine learning and multi-scale modeling to characterize the dynamic growth and remodeling during heart failure across the scales, from the molecular via the cellular to the cardiac level 83.
- We have pioneered two-scale dynamic models where the two scale continuously inform each other to simulate Material degradation, Crack initiation, Crack growth and Crack coalescence.
- In ordinary differential equation modeling, we often have to rely on classical data acquisition techniques, for example, microscopy or spectroscopy, which are known to have limited temporal resolution.
- The results enable prediction of the macroscopic behavior by the macro structural analysis.
- It defines a “stress” function to optimize, considering a monotonically increasing function f.
- This includes automatic mesh generation, meshless interpolation, and parameterization of the domain itself as one of the inputs for the machine learning algorithms.
- Timecausgabor filters work like special magnifying glasses that zoom in and out on different parts of your data, but they make sure to only look at the past and present, not the future.