Molecular dynamics (MD) simulations provide atomistic insight into biomolecular systems but are often limited by high computational costs required to access long timescales. Coarse-grained machine learning models offer a promising avenue for accelerating sampling, yet conventional force matching approaches often fail to capture the full thermodynamic landscape as fitting a model on the gradient may not fit the absolute differences between low-energy conformational states. In this work, we incorporate a complementary energy matching term into the loss function. We evaluate our framework on the Chignolin protein using the CGSchNet model, systematically varying the weight of the energy loss term. While energy matching did not yield statistically significant improvements in accuracy, it revealed distinct tendencies in how models generalize the free energy surface. Our results suggest future opportunities to enhance coarse-grained modeling through improved energy estimation techniques and multi-modal loss formulations.

Belanger & McCallum (2016) and Gygli et al. (2017) have shown that energy In this work, we propose Structured Energy As Loss (SEAL) to take advantage of the expressivity of energy networks without incurring the high inference cost. This raises a question: Can energy networks be used in a way that is as expressive as SPENs, as efficient at inference as feedforward approaches, and also easy to train?

The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally activated events within the harmonic approximation of transition state theory. When combined directly with electronic structure calculations, the number of energy and atomic force evaluations needed for convergence is a primary issue. Here, we describe an efficient implementation of Gaussian process regression (GPR) acceleration of the minimum mode following method where a dimer is used to estimate the lowest eigenmode of the Hessian. A surrogate energy surface is constructed and updated after each electronic structure calculation. The method is applied to a test set of 500 molecular reactions previously generated by Hermez and coworkers [J. Chem. Theory Comput. 18, 6974 (2022)]. An order of magnitude reduction in the number of electronic structure calculations needed to reach the saddle point configurations is obtained by using the GPR compared to the dimer method. Despite the wide range in stiffness of the molecular degrees of freedom, the calculations are carried out using Cartesian coordinates and are found to require similar number of electronic structure calculations as an elaborate internal coordinate method implemented in the Sella software package. The present implementation of the GPR surrogate model in C++ is efficient enough for the wall time of the saddle point searches to be reduced in 3 out of 4 cases even though the calculations are carried out at a low Hartree-Fock level.

In this study we introduce a novel energy functional for long-sequence memory, building upon the framework of dense Hopfield networks which achieves exponential storage capacity through higher-order interactions. Building upon earlier work on long-sequence Hopfield memory models, we propose a temporal kernal $K(m, k)$ to incorporate temporal dependencies, enabling efficient sequential retrieval of patterns over extended sequences. We demonstrate the successful application of this technique for the storage and sequential retrieval of movies frames which are well suited for this because of the high dimensional vectors that make up each frame creating enough variation between even sequential frames in the high dimensional space. The technique has applications in modern transformer architectures, including efficient long-sequence modeling, memory augmentation, improved attention with temporal bias, and enhanced handling of long-term dependencies in time-series data. Our model offers a promising approach to address the limitations of transformers in long-context tasks, with potential implications for natural language processing, forecasting, and beyond.

The accuracy of density functional theory hinges on the approximation of non-local contributions to the exchange-correlation (XC) functional. To date, machine-learned and human-designed approximations suffer from insufficient accuracy, limited scalability, or dependence on costly reference data. To address these issues, we introduce Equivariant Graph Exchange Correlation (EG-XC), a novel non-local XC functional based on equivariant graph neural networks. EG-XC combines semi-local functionals with a non-local feature density parametrized by an equivariant nuclei-centered point cloud representation of the electron density to capture long-range interactions. By differentiating through a self-consistent field solver, we train EG-XC requiring only energy targets. In our empirical evaluation, we find EG-XC to accurately reconstruct `gold-standard' CCSD(T) energies on MD17. On out-of-distribution conformations of 3BPA, EG-XC reduces the relative MAE by 35% to 50%. Remarkably, EG-XC excels in data efficiency and molecular size extrapolation on QM9, matching force fields trained on 5 times more and larger molecules. On identical training sets, EG-XC yields on average 51% lower MAEs.

Novel, functional structures at the nanoscale could be crucial for transforming a broad spectrum of economically significant processes into greener and more sustainable solutions. For instance, nanostructured materials hold the potential to significantly enhance the cost-effectiveness of fuel-cell devices [1], enable the creation of highly efficient quantum-dot LEDs [2], and pave the way for generating atom-precise efficient nanocatalysts for studying novel catalytic pathways in electrochemical applications [3, 4]. As performance is highly dependent on specific structural characteristics which often can not easily be resolved in lab experiments, computational chemistry - most often by using Density Functional Theory (DFT) based approaches - can be used to generate in-silico insights. Typical questions range from elucidating which feature of a given nanoparticle might improve catalytic performance to mechanistic explanations for key synthesis procedures, allowing tailored experiments to drive up experimental yields for optimal structures. Commonly, these questions are associated with finding energetically favorable configurations for the potential energy surface (PES) of a system, which is a property relevant to solving a wide range of problems in computational chemistry. The established methodology allows finding "docking" mechanisms between small molecules and large biomolecules, which is relevant for drug development [5]. Additionally, a large area of research revolves around the sensing of harmful gases by novel nanomaterials chosen according to their strength of interactions.

The optimization of atomic structures plays a pivotal role in understanding and designing materials with desired properties. However, conventional methods often struggle with the formidable task of navigating the vast potential energy surface, especially in high-dimensional spaces with numerous local minima. Recent advancements in machine learning-driven surrogate models offer a promising avenue for alleviating this computational burden. In this study, we propose a novel approach that combines the strengths of universal machine learning potentials with a Bayesian approach of the GOFEE/BEACON framework. By leveraging the comprehensive chemical knowledge encoded in pretrained universal machine learning potentials as a prior estimate of energy and forces, we enable the Gaussian process to focus solely on capturing the intricate nuances of the potential energy surface. We demonstrate the efficacy of our approach through comparative analyses across diverse systems, including periodic bulk materials, surface structures, and a cluster.

Theoretical studies on chemical reaction mechanisms have been crucial in organic chemistry. Traditionally, calculating the manually constructed molecular conformations of transition states for chemical reactions using quantum chemical calculations is the most commonly used method. However, this way is heavily dependent on individual experience and chemical intuition. In our previous study, we proposed a research paradigm that uses enhanced sampling in QM/MM molecular dynamics simulations to study chemical reactions. This approach can directly simulate the entire process of a chemical reaction. However, the computational speed limits the use of high-precision potential energy functions for simulations. To address this issue, we present a scheme for training high-precision force fields for molecular modeling using our developed graph-neural-network-based molecular model, molecular configuration transformer. This potential energy function allows for highly accurate simulations at a low computational cost, leading to more precise calculations of the mechanism of chemical reactions. We have used this approach to study a Cope rearrangement reaction and a Carbonyl insertion reaction catalyzed by Manganese. This "AI+Physics" based simulation approach is expected to become a new trend in the theoretical study of organic chemical reaction mechanisms.

Biased enhanced sampling methods utilizing collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to high intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While methods like temperature-accelerated molecular dynamics (TAMD) can adopt many CVs in a simulation, unbiasing the simulation requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We test the score-based diffusion unbiasing method on TAMD simulations. The results demonstrate that this unbiasing approach significantly outperforms traditional unbiasing methods, and can generate accurate unbiased conformational ensembles for simulations with a number of CVs higher than usual ranges.