|
1 | | ---- |
2 | | -layout: homepage |
3 | | ---- |
4 | | - |
5 | | -<div style="text-align: center;"> |
6 | | - |
7 | | -<h1>CROKE</h1> |
8 | | - |
9 | | -<h2>Characteristic mapping for Kinetic Equations: from theory to simulations and Reduced Order methods</h2> |
10 | | - |
11 | | -</div> |
12 | | - |
13 | | -In this project, we introduce the characteristic mapping method to address the complexity of high- |
14 | | -dimensional kinetic equations, such as those involving ion-electron interactions in plasma fusion, by integrating mathematical modeling with high-performance computing. This semi-Lagrangian method achieves |
15 | | -exponential resolution in linear time, revealing fine-scale details of the solutions and providing insights into |
16 | | -the filamentation structure of plasmas. By employing reduced-order models, we significantly lower the |
17 | | -numerical complexity of the computations. Our approach, which combines dimensionality reduction of |
18 | | -sub-maps with refinement through map compositions via the solution operator, is innovative and paves the |
19 | | -way for efficient evaluation of high-dimensional distribution functions across extended time intervals and |
20 | | -multi-scale spatial domains. This project is designed to test the potential to enhance existing semi-Lagrangian |
21 | | -techniques and advance our understanding of intricate local thermodynamic non-equilibrium phenomena in |
22 | | -plasmas, with applications in magnetically confined fusion. |
23 | | - |
24 | | -### Team: |
25 | | - |
26 | | -**LAGA, UMR 7030, Université Paris 13** |
27 | | -<br> |
28 | | -Olivier Lafitte (PI and coordinator) |
29 | | - |
30 | | -**CEA - IRFM, Cadarache** |
31 | | -<br> |
32 | | -Kevin Obrejan and Philipp Krah |
33 | | - |
34 | | -**I2M, UMR 7373, Aix-Marseille Université** |
35 | | -<br> |
36 | | -Kai Schneider |
37 | | - |
38 | | -**McGill University, Montreal** |
39 | | -<br> |
40 | | -Jean-Christophe Nave |
41 | | - |
42 | | - |
43 | | -### PhD - Positions Available: |
44 | | - |
45 | | -Contact: [philipp.krah@cea.fr](mailto:philipp.krah@cea.fr) |
46 | | - |
47 | | - |
48 | | ---- |
49 | | - |
| 1 | +--- |
| 2 | +layout: homepage |
| 3 | +--- |
| 4 | + |
| 5 | +<div style="text-align: center;"> |
| 6 | + |
| 7 | +<h1>CROKE</h1> |
| 8 | + |
| 9 | +<h2>-Characteristic mapping for Kinetic Equations-</h2> <br> |
| 10 | +<h3> from theory to simulations and Reduced Order methods </h3> |
| 11 | + |
| 12 | +</div> |
| 13 | + |
| 14 | +In this project, we introduce the characteristic mapping method to address the complexity of high- |
| 15 | +dimensional kinetic equations, such as those involving ion-electron interactions in plasma fusion, by integrating mathematical modeling with high-performance computing. This semi-Lagrangian method achieves |
| 16 | +exponential resolution in linear time, revealing fine-scale details of the solutions and providing insights into |
| 17 | +the filamentation structure of plasmas. By employing reduced-order models, we significantly lower the |
| 18 | +numerical complexity of the computations. Our approach, which combines dimensionality reduction of |
| 19 | +sub-maps with refinement through map compositions via the solution operator, is innovative and paves the |
| 20 | +way for efficient evaluation of high-dimensional distribution functions across extended time intervals and |
| 21 | +multi-scale spatial domains. This project is designed to test the potential to enhance existing semi-Lagrangian |
| 22 | +techniques and advance our understanding of intricate local thermodynamic non-equilibrium phenomena in |
| 23 | +plasmas, with applications in magnetically confined fusion. |
| 24 | + |
| 25 | +## Team: |
| 26 | + |
| 27 | +**LAGA, UMR 7030, Université Paris 13** |
| 28 | +<br> |
| 29 | +Olivier Lafitte (PI and coordinator) |
| 30 | + |
| 31 | +**CEA - IRFM, Cadarache** |
| 32 | +<br> |
| 33 | +Kevin Obrejan and Philipp Krah |
| 34 | + |
| 35 | +**I2M, UMR 7373, Aix-Marseille Université** |
| 36 | +<br> |
| 37 | +Kai Schneider |
| 38 | + |
| 39 | +**McGill University, Montreal** |
| 40 | +<br> |
| 41 | +Jean-Christophe Nave |
| 42 | + |
| 43 | + |
| 44 | +## Positions Available: |
| 45 | + |
| 46 | +### Master projects: |
| 47 | + |
| 48 | +We are looking for talented and motivated master students in computational physics, applied mathematics or data-science. |
| 49 | +The proposed Master’s projects can be carried out either as a 6-month internship or as part of a Master’s thesis. |
| 50 | +These projects are funded, and we only accept Master’s students who are interested in pursuing a PhD afterwards. |
| 51 | + |
| 52 | +The projects can take place within one of three teams: CEA, LAGA–Paris, or I2M (Aix-Marseille University). |
| 53 | + |
| 54 | +- Evolving flow maps using neural-semi Lagrangian method: [Proposal](https://characteristicmappingmethod.github.io/assets/projects/neural_SL_CMM.pdf) |
| 55 | +- Data-assimilation for plasma simulations: [Proposal](https://characteristicmappingmethod.github.io/assets/projects/adjoint_plasma.pdf) |
| 56 | +- Learning neural flow maps for drift kinetic equations: [Proposal] |
| 57 | + |
| 58 | +### PhD positions: |
| 59 | + |
| 60 | +Two PhD positions are available that can take place in one of our teams. |
| 61 | + |
| 62 | +For interested candidates please contact: |
| 63 | +[philipp.krah@cea.fr](mailto:philipp.krah@cea.fr) |
| 64 | + |
| 65 | +--- |
| 66 | + |
50 | 67 | [Visit the old Adaptive-CMM project →]({{ '/adaptive-cmm/' | relative_url }}) |
0 commit comments