Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models presents a substantial challenge, either due to the high computational requirements of model-based approaches or the limited robustness of deep learning (DL) methods. We propose a novel framework that leverages the unique strengths of both approaches in a synergistic manner. Our method incorporates a DL ensemble for initial parameter estimation, facilitating efficient downstream evolutionary sampling initialized with this DL-based prior. We showcase the effectiveness of integrating a rapid deep-learning algorithm with a high-precision evolution strategy in estimating brain tumor cell concentrations from magnetic resonance images. The DL-Prior plays a pivotal role, significantly constraining the effective sampling-parameter space. This reduction results in a fivefold convergence acceleration and a Dice-score of 95%.

翻译：生物物理建模，特别是涉及偏微分方程（PDEs）的模型，在根据个体患者定制疾病治疗方案方面展现出巨大潜力。然而，这些模型的逆问题求解环节构成了重大挑战，其原因要么是基于模型的方法计算需求过高，要么是深度学习（DL）方法的鲁棒性有限。我们提出了一种新颖的框架，以协同方式融合了两种方法的独特优势。我们的方法引入一个DL集成模型进行初始参数估计，从而促进基于此DL先验初始化的高效下游进化采样。我们展示了将快速深度学习算法与高精度进化策略相结合，在从磁共振图像估计脑肿瘤细胞浓度方面的有效性。DL-Prior发挥了关键作用，显著约束了有效的采样参数空间。这种缩减带来了五倍的收敛加速，并实现了95%的Dice分数。