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Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity

ICML 2025 · Architectures and efficiency › RNNs and normalization · approach: Scalable approximation and equivariant compute · 0 citations (OpenAlex)

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Proposes SPHNet, an SE(3)-equivariant Hamiltonian predictor that uses learned sparse pair and tensor-product gates plus a three-phase sparsity scheduler to cut tensor product cost while keeping accuracy.

Problem

Predicting DFT Hamiltonian matrices with SE(3) equivariant networks is bottlenecked by the quadratic number of atom pairs and the high-order tensor product costs, which limit scalability to large molecules and large basis sets.

Approach

Adaptive sparsity via two learnable gates: a Sparse Pair Gate that selects important atom pairs and a Sparse TP Gate that prunes cross-order Clebsch-Gordan combinations, trained with a three-phase (random, top-k adaptive, fixed) scheduler.

Key results

• On PubChemQH, SPHNet reports 7.1x speedup over QHNet with Hamiltonian MAE 97.31 vs 123.74 (10^-6 Eh) and memory 5.62 vs 22.5 GB/sample.
• On QH9 stable-iid, SPHNet reaches 4.0x speedup over QHNet and lower Hamiltonian MAE (45.48 vs 76.31).
• Sparsity sweep shows accuracy stable up to about 70% sparsity on PubChemQH, with MAE rising sharply at 80% (158.70).

Measured effects reported in the paper

Surprising findings

• Removing one Pair Construction block barely hurts PubChemQH accuracy (89.17 vs 86.35), suggesting room for further speedup.
• Selected tensor-product combinations show output-order selection ratios that decrease monotonically with order in the non-diagonal block.

Limitations

• WANet was not open-sourced, so comparisons with it are limited to numbers reported in its paper.
• Gains on MD17 are small because baselines already perform well and small molecules have few interaction combinations to prune.
• Sparsity rate must be chosen per dataset (0.1 to 0.7) using system size heuristics; accuracy degrades sharply past the threshold.

Experimental setup

Datasets: QH9 PubChemQH MD17

Benchmarks: QH9 PubChemQH MD17

Metrics: Hamiltonian MAE occupied orbital energy MAE orbital coefficient cosine similarity training memory per sample training speed speedup ratio

Baselines: QHNet WANet PhiSNet SchNOrb

Builds on: QHNet e3nn SE(3)-Transformer Lottery Ticket Hypothesis

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