A Data Driven Method for Computing Quasipotentials

The paper states, as Theorem 1, that if f admits an orthogonal decomposition f = −∇V + g with ∇V·g = 0 and V has a strict local minimum on an attractor A, then within the sublevel set S = {x : V(x) ≤ min∂D V}, the quasipotential UA coincides with 2V up to an additive constant; the proof is deferred to Freidlin–Wentzell ("Proof. See Ref. [1]") . The candidate solution supplies a constructive proof sketch: it rewrites the Freidlin–Wentzell action A[φ;T] via F := ∇V + g and obtains an identity A[φ;T] = 2(V(φ(T)) − V(φ(0))) + (1/2)∫|φ̇ − F(φ)|^2 dt, yielding matching lower and upper bounds by calibrating along F-orbits. This matches the paper’s statement and standard setup (SDE, action functional, quasipotential definition) presented in Section 2 . The paper’s claim is correct but cites an external source for the proof; the model’s solution is also correct at the level of a proof sketch, with minor technical points (e.g., the connector from A when ∇V=0 on A and handling boundary points) that are readily addressed.