Taming Gradient Perturbations: Probabilistic Reparameterization for Robust Physics-Informed MRI Protocol Optimization

Reliable estimation of tissue characteristics in quantitative MRI depends on optimizing acquisition protocols defined by combinations of control parameters. Existing physics-informed optimization methods rely on gradient-based updates, but are highly sensitive to stochastic noise arising from both the imaging system and stochastic gradient descent (SGD), often leading to unstable updates and suboptimal solutions in combinatorial control parameter spaces. To address this, we present Robust Physics-Informed Optimization (RPO), a noise-robust framework that replaces direct optimization of control parameter values with probabilistic optimization over candidate control parameters. Specifically, RPO introduces a probabilistic reparameterization of the control parameters via the Gumbel-Softmax mapping, thereby changing how gradient perturbations propagate through the Jacobian of the mapping. Theoretically, this reparameterization attenuates gradient perturbations, yielding an operator-norm bound proportional to $1/\tau$ and providing a mechanistic explanation for robustness to system noise and SGD-induced stochasticity. Furthermore, the temperature parameter $\tau$ shapes the optimization dynamics by balancing broad exploration of candidate configurations in the early iterations with progressively sharper focus on high-probability solutions. Extensive experiments on both simulated and in vivo MRI data demonstrate that RPO consistently improves optimization robustness and tissue-estimation accuracy under realistic noise conditions, with successful translation to actual MRI systems.