Related papers: A new mathematical model for molecular dynamics 1:…
We consider the Allen-Cahn equations with memory (a partial integro-differential convolution equation). The prototype kernels are exponentially decreasing functions of time and they reduce the integrodifferential equation to a hyperbolic…
Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the timescales necessary to capture the structural evolution…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
We first review traditional approaches to memory storage and formation, drawing on the literature of quantitative neuroscience as well as statistical physics. These have generally focused on the fast dynamics of neurons; however, there is…
It is shown that a small subset of modes which are likely to be involved in protein functional motions of large amplitude can be determined by retaining the most robust normal modes obtained using different protein models. This result…
Molecular dynamics (MD) is a powerful technique for studying microscopic phenomena, but its computational cost has driven significant interest in the development of deep learning-based surrogate models. We introduce generative modeling of…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
A wide array of biological systems can navigate in shallow gradients of chemoattractant with remarkable precision. Whilst previous approaches model such systems using coarse-grained chemical density profiles, we construct a dynamical model…
We consider the class of Hopfield models of associative memory with activation function $F$ and state space $\{-1,1\}^N$, where each vertex of the cube describes a configuration of $N$ binary neurons. $M$ randomly chosen configurations,…
We present the construction of molecular force fields for small molecules (less than 25 atoms) using the recently developed symmetrized gradient-domain machine learning (sGDML) approach [Chmiela et al., Nat. Commun. 9, 3887 (2018); Sci.…
Proteins play crucial roles in every cellular process by interacting with each other, with nucleic acids, metabolites, and other molecules. The resulting assemblies can be very large and intricate and pose challenges to experimental…
LLMs are trained once, then deployed into a world that never stops changing. External memory compensates for this, but most systems manage it explicitly rather than letting it adapt on its own. Biological memory works differently: coupled…
The charge transfer and polarization effects are important components in the molecular mechanism description of bio-molecules. Classical force field with fixed point charge cannot take into the account of the non-negligible correlation…
Intracellular transport processes are essential to the healthy development of many organisms as well as more generally to healthy cellular function. The complex dynamics and interactions between protein molecules and filaments on different…
Conventional molecular dynamics simulations macromolecules require long computational times because the most interesting motions are very slow compared with the fast oscillations of bond lengths and bond angles that limit the integration…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
Posttranslational modifications (PTMs) are an integral component to how cells respond to perturbation. While experimental advances have enabled improved PTM identification capabilities, the same throughput for characterizing how structural…