Method classes
High-level taxonomy used across this website. Each row links to the Research table with a class filter.
| Method class | # papers | Core objective (template) | |
|---|---|---|---|
| PINN / physics-constrained | 143 | \[u_\theta = \mathrm{NN}_\theta(x,t)\\qquad \mathcal{N}[u]=0\ \text{(PDE residual)}\]
\[\min_\theta\ \underbrace{\|u_\theta- u_{data}\|^2}_{\mathcal{L}_{data}} + \lambda\underbrace{\|\mathcal{N}[u_\theta]\|^2}_{\mathcal{L}_{PDE}} + \mu\underbrace{\|\mathcal{B}[u_\theta]\|^2}_{\mathcal{L}_{BC/IC}}\] | View papers |
| Operator learning | 81 | \[G_\theta: a(\cdot)\mapsto u(\cdot)\ \ \text{(solution operator)}\]
\[\min_\theta\ \sum_i \|G_\theta(a_i)-u_i\|^2\ \ \text{(+ optional physics / residual regularization)}\] | View papers |
| SciML | 44 | \[\text{A broad bucket: see the method class tags for the closest training objective.}\] | View papers |
| Graph / mesh | 13 | \[h_i^{(\ell+1)} = \phi\Big(h_i^{(\ell)},\ \sum_{j\in\mathcal{N}(i)} \psi(h_i^{(\ell)},h_j^{(\ell)},e_{ij})\Big)\]
\[\min_\theta\ \sum_t\ \|u_{t+1}-\mathrm{GNN}_\theta(u_t,\text{mesh})\|^2\ \ \text{(rollout / one-step)}\] | View papers |
| Diffusion | 12 | \[x_t = \alpha(t)\,x_0 + \sigma(t)\,\epsilon\ ,\ \epsilon\sim\mathcal{N}(0,I)\]
\[\min_\theta\ \mathbb{E}_{t,x_0,\epsilon}\ \|\epsilon-\epsilon_\theta(x_t,t,c)\|^2\ \ \text{(conditioning }c: \text{measurements/masks)}\] | View papers |
| Benchmark | 4 | \[\text{(No single method.) Benchmarks define datasets, masks, metrics, and protocols.}\] | View papers |
| Transformers | 3 | \[\mathrm{Attn}(Q,K,V)=\mathrm{softmax}(QK^\top/\sqrt{d})V\ \ \text{(global token mixing)}\] | View papers |
| CNN / U-Net | 1 | \[\text{A broad bucket: see the method class tags for the closest training objective.}\] | View papers |
Baseline methods (curated pages)
Baseline lists are only available on manually curated paper pages. This table summarizes what is currently extracted.