noise reduction

Author: ChrisRackauckas

DelayLotkaVolterra/VolterraExp.jl

@@ -32,7 +32,7 @@ plot!(solution, alpha = 0.5)
 # Ideal data
 tsdata = Array(solution)
 # Add noise to the data
-noisy_data = tsdata + Float32(1e-4)*randn(eltype(tsdata), size(tsdata))
+noisy_data = tsdata + Float32(1e-5)*randn(eltype(tsdata), size(tsdata))
 
 plot(abs.(tsdata-noisy_data)')
 
@@ -133,7 +133,7 @@ basis = Basis(h, u)
 # Create an optimizer for the SINDY problem
 opt = SR3()
 # Create the thresholds which should be used in the search process
-λ = exp10.(-10:0.1:3)
+λ = exp10.(-6:0.1:2)
 # Target function to choose the results from; x = L0 of coefficients and L2-Error of the model
 f_target(x, w) = iszero(x[1]) ? Inf : norm(w.*x, 2)
 
@@ -143,12 +143,12 @@ println(Ψ)
 print_equations(Ψ)
 
 # Test on ideal derivative data ( not available )
-Ψ = SInDy(X[:, 5:end], L[:, 5:end], basis, λ, opt = opt, maxiter = 10000, f_target = f_target) # Suceed
+Ψ = SInDy(X[:, 5:end], L[:, 5:end], basis, λ, opt = opt, maxiter = 10000, f_target = f_target) # Succeed
 println(Ψ)
 print_equations(Ψ)
 
 # Test on uode derivative data
-Ψ = SInDy(noisy_data[:, 2:end], L̂[:, 2:end], basis, λ,  opt = opt, maxiter = 100000, normalize = true, denoise = true, f_target = f_target) # Suceed
+Ψ = SInDy(X[:, 2:end], L̂[:, 2:end], basis, λ,  opt = opt, maxiter = 10000, normalize = true, denoise = true, f_target = f_target) # Succeed
 println(Ψ)
 print_equations(Ψ)
 p̂ = parameters(Ψ)
@@ -161,7 +161,7 @@ unknown_eq = ODEFunction(unknown_sys)
 # Just the equations
 b = Basis((u, p, t)->unknown_eq(u, [1.; 1.], t), u)
 # Retune for better parameters -> we could also use DiffEqFlux or other parameter estimation tools here.
-Ψf = SInDy(noisy_data[:, 2:end], L̂[:, 2:end], b, opt = SR3(0.01), maxiter = 100, convergence_error = 1e-18) # Suceed
+Ψf = SInDy(noisy_data[:, 2:end], L̂[:, 2:end], b, opt = SR3(0.01), maxiter = 100, convergence_error = 1e-18) # Succeed
 println(Ψf)
 p̂ = parameters(Ψf)