Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Solving High-Dimensional PDEs with Latent Spectral Models
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add neural spectral block (vs. none) (ablation) | LSM · Elasticity-P | MSE: 0.0253 -> 0.0218 | Helped |
| add neural spectral block (vs. none) (ablation) | LSM · Darcy | MSE: 0.0075 -> 0.0065 | Helped |
| add attention-based projector (vs. removing it) (ablation) | LSM · Elasticity-P | MSE: 0.0563 -> 0.0218 | Helped |
| add multiscale architecture (ablation) | LSM · Darcy | MSE: 0.0123 -> 0.0065 | Helped |
| add patchify operation (ablation) | LSM · Elasticity-P | MSE: 0.0545 -> 0.0218 | Helped |
| replace attention projector with convolution (ablation) | LSM · Elasticity-P | MSE: 0.0218 -> 0.0236 | Hurt |
| replace attention projector with self-attention (ablation) | LSM · Elasticity-P | MSE: 0.0218 -> 0.0245 | Hurt |
| replace attention projector with average pooling (ablation) | LSM · Elasticity-P | MSE: 0.0218 -> 0.0243 | Hurt |
| replace neural spectral block with FNO (ablation) | LSM · Elasticity-P | MSE: 0.0218 -> 0.0356 | Hurt |
| replace trigonometric basis with polynomial basis (ablation) | LSM · Elasticity-P | MSE: 0.0218 -> 0.0261 | Hurt |
| replace neural spectral block with MLP (ablation) | LSM · Elasticity-P | MSE: 0.0253 -> 0.0249 (MLP) vs 0.0218 full | No clear effect |
| LSM hierarchical projection and spectral design overall vs previous SOTA | LSM · Seven PDE benchmarks | MSE relative error reduction: 11.5% average relative gain | Helped |
Closest papers by meaning
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- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs (NeurIPS 2025 · similarity 0.88)
- Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equations (ICML 2025 · similarity 0.88)
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