# Hessian-informed machine learning interatomic potential towards bridging theory and experiments

arXiv: https://arxiv.org/abs/2603.25373 · HTML: https://mlsanity.com/paper/2603.25373/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 75 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics](https://mlsanity.com/paper/1712.03641/) (2017)
- [Open Materials 2024 (OMat24) Inorganic Materials Dataset and Models](https://mlsanity.com/paper/2410.12771/) (2024)
- [Transition1x -- a Dataset for Building Generalizable Reactive Machine Learning Potentials](https://mlsanity.com/paper/2207.12858/) (2022)
- [86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy](https://mlsanity.com/paper/2004.11658/) (2020)
- [HIP: Hessian Interatomic Potentials without derivatives](https://mlsanity.com/paper/2509.21624/) (2025)
- [Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems](https://mlsanity.com/paper/2504.06087/) (2025)
- [Hessian QM9: A quantum chemistry database of molecular Hessians in implicit solvents](https://mlsanity.com/paper/2408.08006/) (2024)
- [PFT: Phonon Fine-tuning for Machine Learned Interatomic Potentials](https://mlsanity.com/paper/2601.07742/) (2026)
- [Projected Hessian Learning: Fast Curvature Supervision for Accurate Machine-Learning Interatomic Potentials](https://mlsanity.com/paper/2603.04523/) (2026)

## Abstract (arXiv)

Local curvature of potential energy surfaces is critical for predicting certain experimental observables of molecules and materials from first principles, yet it remains far beyond reach for complex systems. In this work, we introduce a Hessian-informed Machine Learning Interatomic Potential (Hi-MLIP) that captures such curvature reliably, thereby enabling accurate analysis of associated thermodynamic and kinetic phenomena. To make Hessian supervision practically viable, we develop a highly efficient training protocol, termed Hessian INformed Training (HINT), achieving two to four orders of magnitude reduction for the requirement of expensive Hessian labels. HINT integrates critical techniques, including Hessian pre-training, configuration sampling, curriculum learning and stochastic projection Hessian loss. Enabled by HINT, Hi-MLIP significantly improves transition-state search and brings Gibbs free-energy predictions close to chemical accuracy especially in data-scarce regimes. Our framework also enables accurate treatment of strongly anharmonic hydrides, reproducing phonon renormalization and superconducting critical temperatures in close agreement with experiment while bypassing the computational bottleneck of anharmonic calculations. These results establish a practical route to enhancing curvature awareness of machine learning interatomic potentials, bridging simulation and experimental observables across a wide range of systems.