# End-to-End Reaction Field Energy Modeling via Deep Learning based Voxel-to-voxel Transform

arXiv: https://arxiv.org/abs/2410.03927 · HTML: https://mlsanity.com/paper/2410.03927/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 57 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 10 of 10)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
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- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability](https://mlsanity.com/paper/1906.03663/) (2019)

## Abstract (arXiv)

In computational biochemistry and biophysics, understanding the role of electrostatic interactions is crucial for elucidating the structure, dynamics, and function of biomolecules. The Poisson-Boltzmann (PB) equation is a foundational tool for modeling these interactions by describing the electrostatic potential in and around charged molecules. However, solving the PB equation presents significant computational challenges due to the complexity of biomolecular surfaces and the need to account for mobile ions. While traditional numerical methods for solving the PB equation are accurate, they are computationally expensive and scale poorly with increasing system size. To address these challenges, we introduce PBNeF, a novel machine learning approach inspired by recent advancements in neural network-based partial differential equation solvers. Our method formulates the input and boundary electrostatic conditions of the PB equation into a learnable voxel representation, enabling the use of a neural field transformer to predict the PB solution and, subsequently, the reaction field potential energy. Extensive experiments demonstrate that PBNeF achieves over a 100-fold speedup compared to traditional PB solvers, while maintaining accuracy comparable to the Generalized Born (GB) model.