T o overcome these issues, LLMServingSim2.0

The implicit solvent approach offers a computationally efficient framework to model solvation effects in molecular simulations. However, its accuracy often falls short compared to explicit solvent models, limiting its use in precise thermodynamic calculations. Recent advancements in machine learning (ML) present an opportunity to overcome these limitations by leveraging neural networks to develop more precise implicit solvent potentials for diverse applications. A major drawback of current ML-based methods is their reliance on force-matching alone, which can lead to energy predictions that differ by an arbitrary constant and are therefore unsuitable for absolute free energy comparisons. Here, we introduce a novel methodology with a graph neural network (GNN)-based implicit solvent model, dubbed Lambda Solvation Neural Network (LSNN). In addition to force-matching, this network was trained to match the derivatives of alchemical variables, ensuring that solvation free energies can be meaningfully compared across chemical species.. Trained on a dataset of approximately 300,000 small molecules, LSNN achieves free energy predictions with accuracy comparable to explicit-solvent alchemical simulations, while offering a computational speedup and establishing a foundational framework for future applications in drug discovery.

This paper presents a residual-informed machine learning approach for replacing algebraic loops in equation-based Modelica models with neural network surrogates. A feedforward neural network is trained using the residual (error) of the algebraic loop directly in its loss function, eliminating the need for a supervised dataset. This training strategy also resolves the issue of ambiguous solutions, allowing the surrogate to converge to a consistent solution rather than averaging multiple valid ones. Applied to the large-scale IEEE 14-Bus system, our method achieves a 60% reduction in simulation time compared to conventional simulations, while maintaining the same level of accuracy through error control mechanisms.

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ABSTRACT It was recently shown that the loss function used for training physics-informed neural networks (PINNs) exhibits local minima at solutions corresponding to fixed points of dynamical systems. In the forward setting, where the PINN is trained to solve initial value problems, these local minima can interfere with training and potentially leading to physically incorrect solutions. Building on stability theory, this paper proposes a regularization scheme that penalizes solutions corresponding to unstable fixed points. Experimental results on four dynamical systems, including the Lotka-V olterra model and the van der Pol oscillator, show that our scheme helps avoiding physically incorrect solutions and substantially improves the training success rate of PINNs. Index T erms-- PINNs, regularization, stability 1. INTRODUCTION Physics-informed neural networks (PINNs, [1]) are among the most prominent instantiations of physics-informed machine learning.

The role of mental simulation in human physical reasoning is widely acknowledged, but whether it is employed across scenarios with varying simulation costs and where its boundary lies remains unclear. Using a pouring-marble task, our human study revealed two distinct error patterns when predicting pouring angles, differentiated by simulation time. While mental simulation accurately captured human judgments in simpler scenarios, a linear heuristic model better matched human predictions when simulation time exceeded a certain boundary. Motivated by these observations, we propose a dual-process framework, Simulation-Heuristics Model (SHM), where intuitive physics employs simulation for short-time simulation but switches to heuristics when simulation becomes costly. By integrating computational methods previously viewed as separate into a unified model, SHM quantitatively captures their switching mechanism. The SHM aligns more precisely with human behavior and demonstrates consistent predictive performance across diverse scenarios, advancing our understanding of the adaptive nature of intuitive physical reasoning.