Research map / Learning theory and algorithms / Matrix and tensor methods
A Deep Conjugate Direction Method for Iteratively Solving Linear Systems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace CG search directions with DCDM network-guided directions (deep conjugate directions) | CG on bunny example, 256^3 grid · Bunny example, 256^3 | iterations to reduce residual 4 orders: 1046 -> 44 iterations (DCDM-128) | Helped |
| Use DCDM instead of CG for linear solve | Bunny example, 256^3 grid · Bunny example, 256^3 | wall-clock time to 4 orders residual reduction: 1548s -> 261-267s | Helped |
| Use DCDM instead of CG on 64^3 grid | Bunny example, 64^3 grid · Bunny example, 64^3 | wall-clock time: CG 1.77s vs DCDM-64 2.71s | Hurt |
| Use FluidNet instead of iterative solve | Bunny example residual reduction · Bunny example, 128^3 and 256^3 | residual reduction: no more than one order of magnitude | Hurt |
| Train on lower resolution (64^3) grid and apply to 256^3 grid (ablation) | DCDM network · Bunny example, 256^3 | residual reduction efficiency | No clear effect |
| Use i_start=k-2 instead of full A-orthogonalization against all prior directions (ablation) | DCDM search direction orthogonalization · Bunny example residual reduction | residual reduction per iteration | No clear effect |
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