Over-PINNs: Enhancing Physics-Informed Neural Networks via Higher-Order Partial Derivative Overdetermination of PDEs

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws directly into the training of neural networks. However, when dealing with complex problems, the accuracy of PINNs still has room for improvement. To address this issue, we introduce the Over-PINNs framework, which leverages automatic differentiation (AD) to generate higher-order auxiliary equations that impose additional physical constraints. These equations are incorporated as extra loss terms in the training process, effectively enhancing the model's ability to capture physical information through an "overdetermined" approach. Numerical results illustrate that this method exhibits strong versatility in solving various types of PDEs. It achieves a significant improvement in solution accuracy without incurring substantial additional computational costs.

A 3D pocket-aware and evolutionary conserved interaction guided diffusion model for molecular optimization

Generating molecules that bind to specific protein targets via diffusion models has shown good promise for structure-based drug design and molecule optimization. Especially, the diffusion models with binding interaction guidance enables molecule generation with high affinity through forming favorable interaction within protein pocket. However, the generated molecules may not form interactions with the highly conserved residues, which are important for protein functions and bioactivities of the ligands. Herein, we developed a new 3D target-aware diffusion model DiffDecip, which explicitly incorporates the protein-ligand binding interactions and evolutionary conservation information of protein residues into both diffusion and sampling process, for molecule optimization through scaffold decoration. The model performance revealed that DiffDecip outperforms baseline model DiffDec on molecule optimization towards higher affinity through forming more non-covalent interactions with highly conserved residues in the protein pocket.

A 3D pocket-aware and affinity-guided diffusion model for lead optimization

Molecular optimization, aimed at improving binding affinity or other molecular properties, is a crucial task in drug discovery that often relies on the expertise of medicinal chemists. Recently, deep learning-based 3D generative models showed promise in enhancing the efficiency of molecular optimization. However, these models often struggle to adequately consider binding affinities with protein targets during lead optimization. Herein, we propose a 3D pocket-aware and affinity-guided diffusion model, named Diffleop, to optimize molecules with enhanced binding affinity. The model explicitly incorporates the knowledge of protein-ligand binding affinity to guide the denoising sampling for molecule generation with high affinity. The comprehensive evaluations indicated that Diffleop outperforms baseline models across multiple metrics, especially in terms of binding affinity.