Deterministic particle flows for constraining SDEs

Resulted in paper Maoutsa \& Opper, Phys. Review Research 2022 with Supplement here.

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Terminal and path constraints for stochastic control - Dimitra Maoutsa, Manfred Opper

Proposed deterministic particle control framework - Dimitra Maoutsa, Manfred Opper

Backward probability flow ODE on LC with only terminal constraints - Dimitra Maoutsa, Manfred Opper

Controlled paths with Van der Pol dynamics with terminal constraint reach the final target, while the uncontrolled paths reach the vicinity without reaching the target. This example is inspired by my subsequent work see here , where the ground truth dynamics (Van der Pol in this example) are not known, but are rather inferred from the invariant density. In this example here the ground thruth dynamics are known and are used to simulate the the path, but without the terminal constraint the paths only end up somewhere near the target state, instead of ending up on it.

Controlled and uncontrolled LC paths with only terminal constraints - Dimitra Maoutsa, Manfred Opper