Summary
A physicality benchmark testing whether a model's predicted forces are conservative: i.e. the gradient of a single underlying energy. Following Bigi, Langer & Ceriotti's "The Dark Side of the Forces" (arXiv:2412.11569), the force Jacobian (∂fᵢ/∂rⱼ) is built by central finite differences and the antisymmetric fraction of its Frobenius norm, λ = ‖J_anti‖ / ‖J‖ where J_anti = (J − Jᵀ)/2, is reported. λ = 0 for a perfectly conservative model and grows towards 1 as forces become non-conservative. This probes what accuracy benchmarks miss. Non-conservative models predict forces directly rather than as gradients of an energy, which is cheaper but breaks energy conservation. The paper shows this causes ill-defined geometry optimization and unstable molecular dynamics, and unlike symmetry breaking, it is hard to detect and correct.
Interactive features
Table
Category
Physicality
Data availability
None required. All ten test structures (eight molecules + a metal + a 2D sheet) are generated in ASE.
Computational cost
Low: a few minutes for the full model suite on CPU (well under a minute of compute per model). Cost scales with degrees of freedom, at 2 × 3N force evaluations per structure.
Additional context
To validate the benchmark, we plan to register a known non-conservative model (an ORB-v3 direct variant) as a positive control, confirming that λ clearly detects non-conservative forces when present.
Summary
A physicality benchmark testing whether a model's predicted forces are conservative: i.e. the gradient of a single underlying energy. Following Bigi, Langer & Ceriotti's "The Dark Side of the Forces" (arXiv:2412.11569), the force Jacobian (∂fᵢ/∂rⱼ) is built by central finite differences and the antisymmetric fraction of its Frobenius norm, λ = ‖J_anti‖ / ‖J‖ where J_anti = (J − Jᵀ)/2, is reported. λ = 0 for a perfectly conservative model and grows towards 1 as forces become non-conservative. This probes what accuracy benchmarks miss. Non-conservative models predict forces directly rather than as gradients of an energy, which is cheaper but breaks energy conservation. The paper shows this causes ill-defined geometry optimization and unstable molecular dynamics, and unlike symmetry breaking, it is hard to detect and correct.
Interactive features
Table
Category
Physicality
Data availability
None required. All ten test structures (eight molecules + a metal + a 2D sheet) are generated in ASE.
Computational cost
Low: a few minutes for the full model suite on CPU (well under a minute of compute per model). Cost scales with degrees of freedom, at 2 × 3N force evaluations per structure.
Additional context
To validate the benchmark, we plan to register a known non-conservative model (an ORB-v3 direct variant) as a positive control, confirming that λ clearly detects non-conservative forces when present.