Add diagnostic framework, S3 adaptive/BIC interpolators, and transcendental UQ

Major additions:
- Diagnostic framework (diagnostics.jl, svg_plots.jl): oracle Taylor coefficients,
  polynomial feasibility, Jacobian sensitivity analysis, and HTML report generation
- S3 adaptive-tolerance and BIC model-selection interpolator variants
- _obs_trfn_ observable transcendental variable support for UQ pipeline
- forced_decay() test model for fast transcendental regression testing

Key fixes:
- GP hyperparameter optimization: replaced Zygote with ForwardDiff (Julia 1.12 compat)
- Removed data jitter from GP fitting (was destroying high-order derivatives)
- Adaptive Cholesky jitter for numerical stability
- SE kernel derivatives: generalized to arbitrary order via Hermite recurrence
- HC.jl variable replacement: two-pass longest-first to prevent substring collisions
- Skip _trfn_ auxiliary observables in interpolant construction (pure waste)
- UQ warnings: negative variance, high condition number, zero-variance data vars

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: orebas

CLAUDE.md

@@ -1,10 +1,12 @@
 # ODEParameterEstimation.jl Guidelines
 
 ## Build/Test Commands
-- Activate the project: `julia --project`
-- Run tests: `julia --project -e "using Pkg; Pkg.test()"`
-- Run specific test: `julia --project test/specific_test.jl`
-- Run examples: `julia --project -e "include(\"src/examples/run_examples.jl\")"`
+- **Always use `--startup-file=no`** when invoking Julia (Revise.jl causes exit segfaults on Julia 1.12)
+- Use global Julia environment (plain `julia`, NOT `julia --project`) for running tests
+- Run tests: `julia --startup-file=no -e 'using ODEParameterEstimation; include("test/fast_core.jl")'`
+- Run feature regressions: `julia --startup-file=no -e 'using ODEParameterEstimation; include("test/feature_regressions.jl")'`
+- Run specific test: `julia --startup-file=no -e 'using ODEParameterEstimation; include("test/specific_test.jl")'`
+- Run examples: `julia --startup-file=no -e 'using ODEParameterEstimation; include("src/examples/run_examples.jl")'`
 
 ## Code Style Guidelines
 - Imports: Group related packages, with ModelingToolkit, OrdinaryDiffEq first

src/ODEParameterEstimation.jl

@@ -34,7 +34,7 @@ using TaylorDiff
 using NonlinearSolve, Symbolics, ForwardDiff, FiniteDiff, LinearAlgebra
 using NLopt, Optim, NLsolve
 using SciMLSensitivity
-using Zygote
+# using Zygote  # Disabled: segfaults Julia 1.12 JIT compiler. ForwardDiff is used instead.
 using Enzyme
 #using OptimizationEnzyme
 using SymbolicUtils
@@ -88,6 +88,8 @@ include("core/optimized_multishot_estimation.jl")  # New optimized workflow
 include("core/derivatives.jl")
 include("core/uncertainty_quantification.jl")  # UQ via GP derivative covariances and IFT
 include("core/sampling.jl")
+include("core/svg_plots.jl")
+include("core/diagnostics.jl")
 include("examples/load_examples.jl")
 
 # Export types
@@ -107,7 +109,7 @@ export unpack_ODE, tag_symbol, create_ordered_ode_system
 export add_relative_noise, sample_problem_data, calculate_error_stats
 export analyze_estimation_result, print_stats_table, cluster_solutions
 export clear_denoms, hmcs, analyze_parameter_estimation_problem, analyze_estimation_result
-export aaad, aaad_in_testing, aaad_old_reliable, AAADapprox, GPRapprox, FHDapprox, nth_deriv_at, aaad_gpr_pivot, fhdn
+export aaad, aaad_in_testing, aaad_old_reliable, AAADapprox, GPRapprox, FHDapprox, nth_deriv, nth_deriv_at, aaad_gpr_pivot, fhdn
 export AGPInterpolator, agp_gpr, agp_gpr_robust, mean_and_var
 export calculate_observable_derivatives, create_interpolants, AbstractInterpolator, FourierSeries, solve_with_nlopt, solve_with_nlopt_testing, solve_with_nlopt_quick, solve_with_fast_nlopt
 export solve_with_hc_parameterized, convert_to_hc_format_with_params, extract_data_variables_from_DD, evaluate_data_vars_at_point
@@ -121,6 +123,12 @@ export calculate_higher_derivatives, calculate_higher_derivative_terms
 # Export transcendental handling
 export detect_transcendentals, transform_pep_for_estimation, TranscendentalInfo
 
+# Export diagnostic functions and types
+export diagnose, diagnose_model, diagnose_derivative_accuracy, diagnose_polynomial_system, diagnose_sensitivity
+export PerfectInterpolant, DiagnosticReport, ComprehensiveDiagnosticReport, DerivativeAccuracyReport, PolynomialFeasibilityReport, SensitivityReport
+export EstimationResultsReport, BacksolveUQReport, UncertaintyReport
+export build_perfect_interpolants, compute_oracle_taylor_coefficients, compute_observable_taylor_coefficients
+
 # Export UQ (Uncertainty Quantification) functions
 export AGPInterpolatorUQ, agp_gpr_uq
 export se_kernel_derivative, se_kernel_prior_covariance_matrix, se_kernel_cross_time_covariance_matrix
@@ -131,7 +139,7 @@ export estimate_parameter_uncertainty, print_uncertainty_results
 # Export example models
 # Simple models
 export simple, simple_linear_combination, onesp_cubed, threesp_cubed
-export lotka_volterra, vanderpol, brusselator, harmonic, fitzhugh_nagumo
+export lotka_volterra, vanderpol, brusselator, harmonic, fitzhugh_nagumo, forced_decay
 export seir, treatment, biohydrogenation, repressilator
 export crauste, seir, daisy_mamil3, daisy_mamil4, hiv
 export substr_test, global_unident_test, sum_test, trivial_unident
@@ -141,11 +149,11 @@ export substr_test, global_unident_test, sum_test, trivial_unident
 export EstimationOptions, SystemSolverMethod, InterpolatorMethod, PolishMethod, EstimationFlow
 export FlowStandard, FlowDirectOpt
 export SolverRS, SolverHC, SolverNLOpt, SolverFastNLOpt, SolverRobust
-export InterpolatorAAAD, InterpolatorAAADGPR, InterpolatorAAADOld, InterpolatorFHD, InterpolatorAGP, InterpolatorAGPRobust, InterpolatorAGPRobustRQ, InterpolatorAGPRobustSEpRQ, InterpolatorAGPRobustSExRQ, InterpolatorAGPRobustMatern52, InterpolatorS2AAAMLE, InterpolatorS3SE, InterpolatorS3RQ, InterpolatorS3SEpRQ, InterpolatorS3SExRQ, InterpolatorS3Matern52, InterpolatorCustom
+export InterpolatorAAAD, InterpolatorAAADGPR, InterpolatorAAADOld, InterpolatorFHD, InterpolatorAGP, InterpolatorAGPRobust, InterpolatorAGPRobustRQ, InterpolatorAGPRobustSEpRQ, InterpolatorAGPRobustSExRQ, InterpolatorAGPRobustMatern52, InterpolatorAGPUQ, InterpolatorS2AAAMLE, InterpolatorS3SE, InterpolatorS3RQ, InterpolatorS3SEpRQ, InterpolatorS3SExRQ, InterpolatorS3Matern52, InterpolatorS3AdaptSE, InterpolatorS3AdaptRQ, InterpolatorS3AdaptSEpRQ, InterpolatorS3AdaptSExRQ, InterpolatorS3AdaptMatern52, InterpolatorS3BICSE, InterpolatorS3BICRQ, InterpolatorS3BICSEpRQ, InterpolatorS3BICSExRQ, InterpolatorS3BICMatern52, InterpolatorCustom
 export PolishNewtonTrust, PolishLevenberg, PolishGaussNewton, PolishBFGS, PolishLBFGS
 export get_solver_function, get_interpolator_function, get_polish_optimizer, get_ad_backend
 export interpolator_method_to_symbol, resolve_interpolator_list, setup_identifiability, compute_shooting_indices
-export is_gp_interpolator, is_matern_interpolator, s3_symbol, s3_refine_gp
+export is_gp_interpolator, is_matern_interpolator, s3_symbol, s3_refine_gp, s3_refine_gp_adaptive, s3_refine_gp_bic
 export merge_options, validate_options, print_options, get_solver_options_dict
 export compatibility_return_code, sync_result_contract!, lineage_summary
 export optimized_multishot_parameter_estimation

src/core/analysis_utils.jl

@@ -407,12 +407,17 @@ function analyze_parameter_estimation_problem(PEP::ParameterEstimationProblem, o
 		end
 		# Use the best solution for UQ
 		best_solution = first(filter(x -> !isnothing(x.err), sort(solved_res, by = x -> isnothing(x.err) ? Inf : x.err)))
+		# Map estimation kernel to UQ kernel (UQ only supports :se and :matern52)
+		_uq_kernel = let k = _gp_kernel_of(opts.interpolator)
+			(k === :matern52) ? :matern52 : :se
+		end
 		uq_result = estimate_parameter_uncertainty(
 			PEP,
 			best_solution,
 			PEP.data_sample;
 			max_deriv_order = 2,
 			n_timepoints = min(20, length(PEP.data_sample["t"]) ÷ 5),
+			kernel_type = _uq_kernel,
 		)
 		uq_result = apply_uq_failure_policy(uq_result, opts)
 		if !opts.nooutput