Deterministic particle flows for constraining SDEs
Resulted in paper Maoutsa \& Opper, Phys. Review Research 2022 with Supplement here.
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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.

