Implicit Neural Representations of Molecular Vector-Valued Functions

2025-02-15

AI Summary

Traditional molecular representations—such as graphs or point clouds—struggle to jointly and continuously encode surface geometry, hydrophobic cores, and dynamic conformational ensembles. To address this, we propose Molecular Neural Fields (MNF): an implicit representation of molecules as vector-valued functions parameterized by neural networks, enabling unified, continuous modeling of shape, hydrophobicity, and atomic composition. This work introduces implicit neural representations to molecular modeling for the first time, overcoming resolution and topological limitations inherent in discrete representations, and yielding compact, differentiable, resolution-agnostic 3D field representations. We employ an auto-decoder for parameterizing protein–ligand complexes and performing super-resolution reconstruction, and an auto-encoder for learning latent volumetric embeddings. Experiments demonstrate MNF’s effectiveness in molecular structure reconstruction, super-resolution recovery, and unbiased spatiotemporal conformational interpolation. MNF establishes a new paradigm for AI-driven molecular design and dynamic simulation.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Molecules have various computational representations, including numerical descriptors, strings, graphs, point clouds, and surfaces. Each representation method enables the application of various machine learning methodologies from linear regression to graph neural networks paired with large language models. To complement existing representations, we introduce the representation of molecules through vector-valued functions, or $n$-dimensional vector fields, that are parameterized by neural networks, which we denote molecular neural fields. Unlike surface representations, molecular neural fields capture external features and the hydrophobic core of macromolecules such as proteins. Compared to discrete graph or point representations, molecular neural fields are compact, resolution independent and inherently suited for interpolation in spatial and temporal dimensions. These properties inherited by molecular neural fields lend themselves to tasks including the generation of molecules based on their desired shape, structure, and composition, and the resolution-independent interpolation between molecular conformations in space and time. Here, we provide a framework and proofs-of-concept for molecular neural fields, namely, the parametrization and superresolution reconstruction of a protein-ligand complex using an auto-decoder architecture and the embedding of molecular volumes in latent space using an auto-encoder architecture.

Problem

• Representing molecules via neural vector fields.
• Capturing molecular features and hydrophobic cores.
• Enabling resolution-independent molecular interpolation.

Innovation

• Neural networks parameterize molecular vector fields
• Auto-decoder architecture for protein-ligand reconstruction
• Auto-encoder embeds molecular volumes in latent space