Machine Learning-Driven Inverse Fluid-Structure Interaction (FSI) Simulations of the Heart*

Current heart fluid-structure interaction (FSI) simulations rely on ex vivo properties, which do not reflect in vivo conditions. To address this, we propose a machine learning-driven approach to solve the inverse FSI problem by identifying properties that match echo images. Our method integrates forward FSI simulations with flow, structural, and electrophysiology solvers. For the inverse problem, we use adjoint methods and convolutional neural networks (CNNs) to minimize discrepancies, validated using elastography-like techniques on a thin rectangular clamped plate with a linear elasticity variation.

We will use a simple multi-layer perceptron (MLP) with two inputs (coordinates) and one output (elasticity), followed by a single neuron with a custom activation function and a constant weight of one to compute the residuals L=R²=g(E(x,y))² . The gradient descent algorithm will optimize the MLP weights and biases to minimize residuals, with the objective​. Using the chain rule,w_i,j=α ∂L/∂w_i,j; ∂L/∂w_i,j=∂L/∂R*∂R/∂E*∂E/∂w_i,j​. The second derivative will be calculated numerically, and the last term will be computed through backpropagation.