Adarsh Pashikanti | Searcharxiv

arXiv2026

Matrix Product Belief Propagation

We introduce "matrix product belief propagation" (MP-BP) as a controlled method for the approximate contraction of two-dimensional tensor networks and graphical models, which generically leads to a quadratic reduction of errors relative to existing methods: at similar computational effort, the number of accurate digits is asymptotically doubled. For infinite systems, MP-BP can be understood as a practical implementation of Baxter's corner-transfer-matrix method; for reflection-symmetric networks, it further coincides with the boundary matrix-product-state and corner-transfer-matrix renormalization group algorithms as conventionally implemented. In the limit of unit matrix-product rank, MP-BP is equivalent to belief propagation, and more generally, can be understood as a generalization of BP in which the "messages" live on surfaces and are assumed to have a matrix-product factorization. We further extend the quadratic improvement to the computation of expectation values, and numerically demonstrate the qualitatively improved convergence for a variety of classical and quantum 2D tensor network problems.

quant-ph↗

arXiv2026

Differentiable Cardiac Electrophysiology Simulations for Dynamical State and Parameter Estimation

The heart's contractions are triggered by action potential waves, which propagate through the cardiac muscle and exhibit diverse spatio-temporal dynamics during different heart rhythms. The dynamics are modeled with partial differential equations (PDEs) in cardiac electrophysiology simulations. However, fitting such models to measurement data to develop digital twins or patient-specific computer models is challenging. Here, we introduce differentiable cardiac electrophysiology simulations that can be fitted automatically to spatio-temporal measurement data of action potential waves in cardiac tissue. By comparing the simulated dynamics with the observation data, we define a loss function that is minimized via gradient-based optimization. Backpropagating the loss gradient through the differentiable PDE solver enables us to learn the parameters and recover the full dynamics, even with sparse, noisy, or partial observations. Implemented using both the finite-difference and smoothed particle hydrodynamics methods, our simulation framework can be applied to pixel-, voxel-, or point-based data, such as 2D or 3D slabs, or arbitrary shapes, such as the heart's ventricles. Using this methodology, we locate early activation sites inside a 3D bi-ventricular simulation geometry and fit a phenomenological model to imaging data of a voltage spiral wave in a cardiac monolayer cell culture. With experimental data, we employed a perceptual loss based on the Video Joint-Embedding Predictive Architecture, which enables fitting to noisy imaging data, and a generative diffusion model to estimate initial conditions and constrain solutions. Differentiable cardiac electrophysiology simulations could improve the diagnosis of rhythm abnormalities in patients and facilitate the development of personalized models or digital twins of the heart.

physics.med-ph↗