Ian Chen

Ian Chen, Alfredo Alexander-Katz

Free energies are fundamental quantities governing phase behavior and thermodynamic stability in polymer systems, yet their accurate computation often requires extensive simulations and post-processing techniques such as the Bennett Acceptance Ratio (BAR). While BAR provides reliable estimates when applied between closely related thermodynamic states, evaluating free energies across large changes in interaction strength typically requires a sequence of intermediate simulations to maintain sufficient phase-space overlap, substantially increasing computational cost. In this work we develop a machine learning framework for rapidly predicting excess free energies of linear diblock copolymer systems from simulation-derived energetic descriptors. Using dissipative particle dynamics simulations of freely-jointed chain polymers, we construct a dataset of per-chain energetic statistics, including heterogeneous interaction energies, homogeneous interaction energies, and bonded spring energies, and train feed-forward neural networks to learn the relationship between these descriptors and free energies computed using a stratified BAR procedure. The resulting models accurately reproduce the reference free energies across a range of chain lengths, compositions, and densities, including polymer architectures held out from training. In regimes where direct, brute-force BAR estimates become unreliable due to poor phase-space overlap, the neural network predictions remain consistent with the reference values. These results demonstrate that physically informed machine learning models can serve as efficient surrogates for expensive free-energy calculations and provide a promising approach for accelerating thermodynamic analysis of polymer systems.

Lei Shi, Ian Chen, Hiroo Takayama et al.

Personalized cardiac mechanics modeling is a powerful tool for understanding the biomechanics of cardiac function in health and disease and assisting in treatment planning. However, current models are limited to using medical images acquired at a single cardiac phase, often limiting their applicability for processing dynamic image acquisitions. This study introduces an inverse finite element analysis (iFEA) framework to estimate the passive mechanical properties of cardiac tissue using time-dependent medical image data. The iFEA framework relies on a novel nested optimization scheme, in which the outer iterations utilize a traditional optimization method to best approximate material parameters that fit image data, while the inner iterations employ an augmented Sellier's algorithm to estimate the stress-free reference configuration. With a focus on characterizing the passive mechanical behavior, the framework employs structurally based anisotropic hyperelastic constitutive models and physiologically relevant boundary conditions to simulate myocardial mechanics. We use a stabilized variational multiscale formulation for solving the governing nonlinear elastodynamics equations, verified for cardiac mechanics applications. The framework is tested in myocardium models of biventricle and left atrium derived from cardiac phase-resolved computed tomographic (CT) images of a healthy subject and three patients with hypertrophic obstructive cardiomyopathy (HOCM). The impact of the choice of optimization methods and other numerical settings, including fiber direction parameters, mesh size, initial parameters for optimization, and perturbations to optimal material parameters, is assessed using a rigorous sensitivity analysis. The performance of the current iFEA is compared against an assumed power-law-based pressure-volume relation, typically used for single-phase image acquisition.