Add bounded coupled damping and prediction-based attempt selection

libmeanfield/interface/solver/newton_numerics.cppm

@@ -53,6 +53,25 @@ export namespace mean_field::solver::nonlinear {
         }
     };
 
+    struct BacktrackedCoupledCurvatureCorrection final {
+        CoupledTrialCorrectionOptions correction{};
+        int maximumAttemptsPerIteration{1};
+        BacktrackedCoupledStep search{};
+        NearAcceptanceCoupledAttempt attempt{};
+
+        void Validate() const {
+            correction.Validate();
+            search.Validate();
+            attempt.Validate();
+            if (maximumAttemptsPerIteration <= 0)
+                throw std::invalid_argument("A coupled trial policy requires a positive attempt budget.");
+        }
+    };
+
+    template <typename Candidate>
+    concept CoupledTrialNumerics = std::same_as<Candidate, CoupledCurvatureCorrection> ||
+                                  std::same_as<Candidate, BacktrackedCoupledCurvatureCorrection>;
+
     template <typename Candidate>
     concept EnthalpyNumerics = std::same_as<Candidate, SampledEnthalpy> ||
                               std::same_as<Candidate, PolynomialEnthalpy>;
@@ -64,7 +83,7 @@ export namespace mean_field::solver::nonlinear {
 
     template <typename Candidate>
     concept TrialPathNumerics = std::same_as<Candidate, UncorrectedTrial> ||
-                                std::same_as<Candidate, CoupledCurvatureCorrection>;
+                                CoupledTrialNumerics<Candidate>;
 
     // Types select algorithms; tolerances and the mesh-dependent work sizes
     // remain runtime data. Adding a strategy cannot silently change a model's