| Project Area | Foundation of "Machine Learning Physics" --- Revolutionary Transformation of Fundamental Physics by A New Field Integrating Machine Learning and Physics |
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| Project/Area Number |
23H04508
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| Research Category |
Grant-in-Aid for Transformative Research Areas (A)
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| Allocation Type | Single-year Grants |
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| Review Section |
Transformative Research Areas, Section (II)
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| Research Institution | Kyoto University |
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Principal Investigator |
MOLINA JOHN 京都大学, 工学研究科, 助教 (20727581)
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| Project Period (FY) |
2023-04-01 – 2025-03-31
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| Project Status |
Granted (Fiscal Year 2024)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2024: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2023: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | Machine Learning / Stokes Flow / Multi-Scale Simulation / Soft Matter / Multi-Scale Simulations / Polymer Melts / Flow Inference / Gaussian Processes |
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| Outline of Research at the Start |
We will improve and optimize the learning methods we have developed for (A) multi-scale simulations of polymer flows and (B) the inference of Stokes flows with missing and/or noisy data. For the former, we will learn the constitutive relation for the canonical polymer entanglement model (i.e., Doi-Takimoto), and use it to simulate the dynamics of entangled polymer melt flows in 2D/3D. For the latter, we will incorporate hydrodynamics stresses and moving boundaries into the inference framework, to consider experimentally relevant flow problems (e.g., biofluids and colloidal dispersions).
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| Outline of Annual Research Achievements |
For theme A, we have succeeded in extending our Gaussian Process (GP) based learning method, originally developed for non-interacting polymers, to entangled polymer melts relevant for industry. In particular, we have learned the (non-linear) constitutive relation of the dual slip-link model, a coarse-grained entanglement model that can explain many of the rheological properties of polymer melts. Our learned model is able to accurately reproduce the flow behavior of entangled polymers (compared to multi-scale simulations) at a small fraction of the cost. This work was published in Physics of Fluids and selected as "Editor's Pick".
For theme B, we have succeeded in developing a probabilistic framework for solving Stokes flow problems, based on a Physics-Informed Gaussian Process regression. We have validated our method on a non-trivial 2D problem: pressure driven flow through a sinusoidal channel. We are able to accurately solve both forward and inverse problems with a high-degree of accuracy. Our method is capable of inferring velocity/pressure fields from partial and/or noisy data, as well as stresses/forces on boundaries. Furthermore, we have shown that our approach is faster and more robust than alternative Machine-Learning solutions, e.g., Physics-Informed Neural Networks.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Our project is progressing smoothly.
We have made progress on both themes, in line with our original plan.
For theme (A), we have extended our method to entangled polymers. Flow predictions using the learned relations are in good agreement with full-scale multi-scale simulations (at a fraction of the cost), even for complex geometries/flows. For theme (B) we have developed a generalized 2D/3D Stokes flow solver. Our method is able to infer physically meaningful flow solutions given sparse/incomplete data, showing that it is a viable candidate for analyzing experiments.
In addition, we have also explored other areas where Physics-Informed Machine Learning approaches can be used to solve Soft Matter flow problems (e.g., autonomous navigation, inferring molecular weights of polymers).
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| Strategy for Future Research Activity |
We will continue to develop themes (A) and (B) to be able to study complex 3D flows.
For theme (A), this requires parallelizing our code for high-performance GPU systems (or hybrid GPU/CPU systems). In particular, we aim to develop efficient parallel data structures to handle the creation/destruction of polymer entanglements within the slip-link model. Furthermore, we will also continue to investigate how to implement data-driven / active learning protocols, to improve the accuracy of our predictions.
For theme (B), we will investigate why the Black-Box Matrix-Matrix method, which is the state-of-the-art for Gaussian Process regression, does not yield the expected performance on our custom physics-informed GP problems. If necessary, we will consider alternative methods, e.g., using different pre-conditioners or dense matrix algorithms. Finally, we will apply our method to experimental 3D data.
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