| 研究領域 | 「学習物理学」の創成－機械学習と物理学の融合新領域による基礎物理学の変革 |
|---|
| 研究課題/領域番号 |
23H04508
|
|---|
| 研究機関 | 京都大学 |
|---|
研究代表者 |
MOLINA JOHN 京都大学, 工学研究科, 助教 (20727581)
|
|---|
| 研究期間 (年度) |
2023-04-01 – 2025-03-31
|
| キーワード | Machine Learning / Multi-Scale Simulations / Polymer Melts / Stokes Flow / Flow Inference / Gaussian Processes |
|---|
| 研究実績の概要 |
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.
|
| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
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).
|
| 今後の研究の推進方策 |
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.
|
