# Memory Force Learning

A fractional grid's observation window misses earlier motion, and that history reaches the future through a memory force. The study separates frequency point prediction from memory reconstruction as two learning objectives: across six-node, ten-cycle, ten-mesh and twenty-mesh cases, a response-trained linear predictor refined by a neural residual lowers frequency RMSE relative to that linear predictor by 0.074 to 0.104 at the primary noise level. A separately reconstructed force serves as the reference for an energy inequality plus an angle test, issuing frequency envelopes in cases where the point predictor alone cannot support them.

A fractional grid's observation window misses earlier motion, and that history reaches the future through a memory force. The study separates frequency point prediction from memory reconstruction as two learning objectives: across six-node, ten-cycle, ten-mesh and twenty-mesh cases, a response-trained linear predictor refined by a neural residual lowers frequency RMSE relative to that linear predictor by 0.074 to 0.104 at the primary noise level. A separately reconstructed force serves as the reference for an energy inequality plus an angle test, issuing frequency envelopes in cases where the point predictor alone cannot support them.