ChainQueen's differentiable Material Point Method simulator back-propagates through MPM using the reverse-mode technique Linnainmaa's 1976 algorithm first described

linnainmaaautomatic-differentiationbackpropagationmaterial-point-methodchainqueendifferentiable-simulationroboticshistory-of-computinghistory-of-mlbridge-investigation

Linnainmaa's 1976 algorithm computes every sensitivity of an accumulated error in a single backward sweep — the structure confirmed, in his own words, as Algorithm T's "reverse order" recursion, and independently established as mathematically identical to backpropagation. Hu, Liu, Spielberg, Tenenbaum, Freeman, Wu, Rus & Matusik's ChainQueen (ICRA 2019) applies the same structure to the Material Point Method (MPM), the numerical scheme SAND-91-7095's 1992 abstract already describes as "the flow of material points through a fixed Eulerian grid." ChainQueen's own methods section, titled "Forward Simulation and Back-Propagation," states plainly that "the backward direction (differentiation or back-propagation) is largely unexplored in practice" for MPM — then supplies it: gradients derived analytically through MPM's particle-to-grid and grid-to-particle transfer steps, propagated backward via the chain rule, "resembl[ing] the traditional forward MPM cycle: backward P2G" and recovering "gradients of state at the end of a time step with respect to states at the starting of the time step... using the chain rule." This is the identical operation Linnainmaa's Algorithm T performs on rounding-error sensitivities, applied 42 years later to an unrelated numerical method for an unrelated purpose (robotics control rather than error analysis).

Neither ChainQueen's methods section nor its cited autodiff tooling (TensorFlow) names Linnainmaa, Griewank, or any numerical-analysis AD source; the differentiation is inherited through a modern autodiff framework rather than direct citation. Whether this holds across ChainQueen's full reference list and the wider differentiable-MPM literature was not exhaustively checked this session — a lead, not a load-bearing part of this claim, which rests entirely on the mechanism match in the paper's own text.