SimpleAdaptiveTauLeaping solver

Project.toml

@@ -4,6 +4,7 @@ authors = ["Chris Rackauckas <accounts@chrisrackauckas.com>"]
 version = "9.25.1"
 
 [deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
@@ -17,6 +18,8 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
+SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 
@@ -54,6 +57,8 @@ RecursiveArrayTools = "3.35, 4"
 Reexport = "1.2"
 SafeTestsets = "0.1"
 SciMLBase = "2.115, 3.1"
+Setfield = "1"
+SimpleNonlinearSolve = "1, 2"
 StableRNGs = "1"
 StaticArrays = "1.9.8"
 Statistics = "1"
@@ -63,7 +68,6 @@ Test = "1"
 julia = "1.10"
 
 [extras]
-ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
@@ -78,4 +82,4 @@ StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["ADTypes", "Aqua", "ExplicitImports", "FastBroadcast", "LinearAlgebra", "LinearSolve", "OrdinaryDiffEq", "Pkg", "SafeTestsets", "StableRNGs", "Statistics", "StochasticDiffEq", "Test"]
+test = ["Aqua", "ExplicitImports", "FastBroadcast", "LinearAlgebra", "LinearSolve", "OrdinaryDiffEq", "Pkg", "SafeTestsets", "StableRNGs", "Statistics", "StochasticDiffEq", "Test"]

src/JumpProcesses.jl

@@ -18,6 +18,9 @@ using StaticArrays: StaticArrays, SVector, setindex
 using Base.Threads: Threads
 using Base.FastMath: add_fast
 
+using SimpleNonlinearSolve: SimpleNonlinearSolve, SimpleNewtonRaphson
+using ADTypes: ADTypes, AutoFiniteDiff
+
 # Import functions we extend from Base
 import Base: size, getindex, setindex!, length, similar, show, merge!, merge
 
@@ -40,7 +43,7 @@ using DiffEqBase: DiffEqBase, CallbackSet, ContinuousCallback, DAEFunction,
                   ODESolution, ReturnCode, SDEFunction, SDEProblem, add_tstop!,
                   deleteat!, isinplace, remake, savevalues!, step!,
                   u_modified!
-using SciMLBase: SciMLBase, DEIntegrator
+using SciMLBase: SciMLBase, DEIntegrator, NonlinearProblem
 
 abstract type AbstractJump end
 abstract type AbstractMassActionJump <: AbstractJump end
@@ -131,7 +134,7 @@ export SSAStepper
 
 # leaping: 
 include("simple_regular_solve.jl")
-export SimpleTauLeaping, SimpleExplicitTauLeaping, EnsembleGPUKernel
+export SimpleTauLeaping, SimpleExplicitTauLeaping, SimpleAdaptiveTauLeaping, NewtonImplicitSolver, TrapezoidalImplicitSolver, EnsembleGPUKernel
 
 # spatial:
 include("spatial/spatial_massaction_jump.jl")

src/simple_regular_solve.jl

@@ -6,6 +6,27 @@ end
 
 SimpleExplicitTauLeaping(; epsilon = 0.05) = SimpleExplicitTauLeaping(epsilon)
 
+# Define solver type hierarchy
+abstract type AbstractImplicitSolver end
+struct NewtonImplicitSolver <: AbstractImplicitSolver end
+struct TrapezoidalImplicitSolver <: AbstractImplicitSolver end
+
+# Adaptive tau-leaping solver
+struct SimpleAdaptiveTauLeaping{T <: AbstractFloat} <: DiffEqBase.DEAlgorithm
+    epsilon::T  # Error control parameter for tau selection
+    solver::AbstractImplicitSolver  # Solver type for implicit method
+    eigenvalue_check::Bool  # Enable eigenvalue-based stiffness detection
+    stiffness_ratio_threshold::T # # Stiffness ratio threshold
+    implicit_epsilon_factor::T  # Scaling factor for implicit tau-selection
+end
+
+# Stiffness detection uses a dynamic threshold epsilon * sum(u) for propensity ratios,
+# as inspired by Cao et al. (2007), Section III.B. Optional eigenvalue-based check
+# uses the Jacobian's eigenvalue ratio. implicit_epsilon_factor=10.0 relaxes tau-selection
+# for implicit tau-leaping, per Cao et al. (2007), Section III.A.
+SimpleAdaptiveTauLeaping(; epsilon=0.05, solver=NewtonImplicitSolver(), eigenvalue_check=false, stiffness_ratio_threshold=1e4, implicit_epsilon_factor=10.0) = 
+    SimpleAdaptiveTauLeaping(epsilon, solver, eigenvalue_check, stiffness_ratio_threshold, implicit_epsilon_factor)
+
 function validate_pure_leaping_inputs(jump_prob::JumpProblem, alg)
     if !(jump_prob.aggregator isa PureLeaping)
         @warn "When using $alg, please pass PureLeaping() as the aggregator to the \
@@ -69,6 +90,20 @@ function _process_saveat(saveat, tspan, save_start, save_end)
     return saveat_vec, _save_start, _save_end
 end
 
+# Validation for adaptive tau-leaping
+function validate_pure_leaping_inputs(jump_prob::JumpProblem, alg::SimpleAdaptiveTauLeaping)
+    if !(jump_prob.aggregator isa PureLeaping)
+        @warn "When using $alg, please pass PureLeaping() as the aggregator to the \
+        JumpProblem, i.e. call JumpProblem(::DiscreteProblem, PureLeaping(),...). \
+        Passing $(jump_prob.aggregator) is deprecated and will be removed in the next breaking release."
+    end
+    isempty(jump_prob.jump_callback.continuous_callbacks) &&
+    isempty(jump_prob.jump_callback.discrete_callbacks) &&
+    isempty(jump_prob.constant_jumps) &&
+    isempty(jump_prob.variable_jumps) &&
+    jump_prob.massaction_jump !== nothing
+end
+
 function DiffEqBase.solve(jump_prob::JumpProblem, alg::SimpleTauLeaping;
         seed = nothing, dt = error("dt is required for SimpleTauLeaping."),
         saveat = nothing, save_start = nothing, save_end = nothing)
@@ -405,6 +440,261 @@ function DiffEqBase.solve(jump_prob::JumpProblem, alg::SimpleExplicitTauLeaping;
     return sol
 end
 
+
+# Compute tau for implicit tau-leaping with relaxed error control
+# Reference: Cao et al. (2007), J. Chem. Phys. 126, 224101, Section III.A
+function compute_tau_implicit(u, rate_cache, nu, hor, p, t, epsilon, rate, dtmin,
+        max_hor, max_stoich, numjumps, implicit_epsilon_factor)
+    tau_explicit = compute_tau(
+        u, rate_cache, nu, hor, p, t, epsilon, rate, dtmin, max_hor, max_stoich, numjumps)
+    u_predict = float.(u)
+    rate(rate_cache, u, p, t)
+    for j in 1:numjumps
+        for spec_idx in 1:size(nu, 1)
+            u_predict[spec_idx] += nu[spec_idx, j] * rate_cache[j] * tau_explicit
+        end
+    end
+    u_predict .= max.(u_predict, zero(eltype(u_predict)))
+    relaxed_epsilon = epsilon * implicit_epsilon_factor
+    tau = compute_tau(u_predict, rate_cache, nu, hor, p, t + tau_explicit,
+        relaxed_epsilon, rate, dtmin, max_hor, max_stoich, numjumps)
+    return max(tau, dtmin)
+end
+
+# Define residual for implicit equation
+# Newton: u_new = u_current + sum_j nu_j * a_j(u_new) * tau (Cao et al., 2004)
+# Trapezoidal: u_new = u_current + sum_j nu_j * (a_j(u_current) + a_j(u_new))/2 * tau
+function implicit_equation!(resid, u_new, params)
+    u_current, rate_cache, nu, p, t, tau, rate, numjumps, solver = params
+    rate(rate_cache, u_new, p, t + tau)
+    resid .= u_new .- u_current
+    if isa(solver, NewtonImplicitSolver)
+        for j in 1:numjumps
+            for spec_idx in 1:size(nu, 1)
+                resid[spec_idx] -= nu[spec_idx, j] * rate_cache[j] * tau  # Cao et al. (2004)
+            end
+        end
+    else  # TrapezoidalImplicitSolver
+        rate_current = similar(rate_cache)
+        rate(rate_current, u_current, p, t)
+        half = one(eltype(rate_cache)) / 2
+        for j in 1:numjumps
+            for spec_idx in 1:size(nu, 1)
+                resid[spec_idx] -= nu[spec_idx, j] * half * (rate_cache[j] + rate_current[j]) * tau
+            end
+        end
+    end
+    resid .= max.(resid, -u_new)  # Ensure non-negative solution
+end
+
+# Solve implicit equation using SimpleNonlinearSolve
+function solve_implicit(u_current, rate_cache, nu, p, t, tau, rate, numjumps, solver)
+    u_new = convert(Vector{float(eltype(u_current))}, u_current)
+    prob = NonlinearProblem(implicit_equation!, u_new, (u_current, rate_cache, nu, p, t, tau, rate, numjumps, solver))
+    sol = solve(prob, SimpleNewtonRaphson(autodiff=AutoFiniteDiff()); abstol=1e-6, reltol=1e-6)
+    return sol.u, sol.retcode == ReturnCode.Success
+end
+
+
+# Compute Jacobian for eigenvalue-based stiffness detection
+# Reference: Cao et al. (2007), Section III.B
+function compute_jacobian(u, rate, numjumps, numspecies, p, t)
+    T = float(eltype(u))
+    sqrteps = sqrt(eps(T))
+    J = zeros(T, numjumps, numspecies)
+    rate_cache = zeros(T, numjumps)
+    rate(rate_cache, u, p, t)
+    rate_plus = zeros(T, numjumps)
+    u_plus = float.(copy(u))
+    for i in 1:numspecies
+        h_i = sqrteps * max(abs(u[i]), one(T))
+        u_plus[i] = u[i] + h_i
+        rate(rate_plus, u_plus, p, t)
+        for j in 1:numjumps
+            J[j, i] = (rate_plus[j] - rate_cache[j]) / h_i
+        end
+        u_plus[i] = u[i]
+    end
+    return J
+end
+
+# Stiffness detection using propensity ratio or eigenvalues
+# Reference: Cao et al. (2007), Section III.B
+function is_stiff(rate_cache, u, epsilon, eigenvalue_check, stiffness_ratio_threshold, p, t, rate, numjumps, numspecies)
+    non_zero_rates = [rate for rate in rate_cache if rate > 0]
+    if length(non_zero_rates) <= 1
+        return false
+    end
+    if eigenvalue_check
+        J = compute_jacobian(u, rate, numjumps, numspecies, p, t)
+        eigvals = real.(LinearAlgebra.eigvals(J))
+        non_zero_eigvals = [abs(λ) for λ in eigvals if abs(λ) > 1e-10]
+        if length(non_zero_eigvals) <= 1
+            return false
+        end
+        max_eig = maximum(non_zero_eigvals)
+        min_eig = minimum(non_zero_eigvals)
+        return max_eig / min_eig > stiffness_ratio_threshold  # Stiffness ratio threshold, Petzold (1983), SIAM J. Sci. Stat. Comput. 4(1), 136–148
+    else
+        max_rate = maximum(non_zero_rates)
+        min_rate = minimum(non_zero_rates)
+        threshold = epsilon * sum(u)
+        return max_rate / min_rate > threshold  # Propensity ratio threshold, Cao et al. (2007), J. Chem. Phys. 126, 224101, Section III.B
+    end
+end
+
+function simple_adaptive_tau_leaping_loop!(
+        prob, alg, u_current, u_new, t_current, t_end, p, rng,
+        rate, nu, hor, max_hor, max_stoich, numjumps, numspecies, epsilon,
+        dtmin, saveat_times, usave, tsave, du, counts, rate_cache, rate_effective, maj,
+        solver, eigenvalue_check, stiffness_ratio_threshold, implicit_epsilon_factor,
+        save_end)
+    save_idx = 1
+
+    while t_current < t_end
+        rate(rate_cache, u_current, p, t_current)
+        if all(<=(0), rate_cache)
+            t_current = t_end
+            break
+        end
+        use_implicit = is_stiff(rate_cache, u_current, epsilon, eigenvalue_check,
+            stiffness_ratio_threshold, p, t_current, rate, numjumps, numspecies)
+        tau = if use_implicit
+            compute_tau_implicit(u_current, rate_cache, nu, hor, p, t_current,
+                epsilon, rate, dtmin, max_hor, max_stoich, numjumps,
+                implicit_epsilon_factor)
+        else
+            compute_tau(u_current, rate_cache, nu, hor, p, t_current,
+                epsilon, rate, dtmin, max_hor, max_stoich, numjumps)
+        end
+        tau = min(tau, t_end - t_current)
+        if !isempty(saveat_times) && save_idx <= length(saveat_times) &&
+           t_current + tau > saveat_times[save_idx]
+            tau = saveat_times[save_idx] - t_current
+        end
+
+        if use_implicit
+            u_new_float, converged = solve_implicit(u_current, rate_cache, nu, p,
+                t_current, tau, rate, numjumps, solver)
+            if !converged
+                tau /= 2
+                continue
+            end
+            rate(rate_cache, u_new_float, p, t_current + tau)
+        end
+
+        rate_effective .= max.(rate_cache .* tau, zero(eltype(rate_cache)))
+        for j in eachindex(counts)
+            if rate_effective[j] <= zero(eltype(rate_effective))
+                counts[j] = zero(eltype(counts))
+            else
+                counts[j] = pois_rand(rng, rate_effective[j])
+            end
+        end
+        du .= zero(eltype(du))
+        for j in 1:numjumps
+            for (spec_idx, stoch) in maj.net_stoch[j]
+                du[spec_idx] += stoch * counts[j]
+            end
+        end
+        u_new .= u_current .+ du
+        if any(<(0), u_new)
+            tau /= 2
+            continue
+        end
+        t_new = t_current + tau
+
+        if isempty(saveat_times) ||
+           (save_idx <= length(saveat_times) && t_new >= saveat_times[save_idx])
+            push!(usave, copy(u_new))
+            push!(tsave, t_new)
+            if !isempty(saveat_times) && t_new >= saveat_times[save_idx]
+                save_idx += 1
+            end
+        end
+
+        u_current .= u_new
+        t_current = t_new
+    end
+
+    if save_end && (isempty(tsave) || tsave[end] != t_end)
+        push!(usave, copy(u_current))
+        push!(tsave, t_end)
+    end
+end
+
+# Adaptive tau-leaping solver
+# Reference: Cao et al. (2007), Cao et al. (2004), Cao et al. (2006)
+function DiffEqBase.solve(jump_prob::JumpProblem, alg::SimpleAdaptiveTauLeaping;
+        seed = nothing,
+        dtmin = nothing,
+        saveat = nothing, save_start = nothing, save_end = nothing)
+    validate_pure_leaping_inputs(jump_prob, alg) ||
+        error("SimpleAdaptiveTauLeaping can only be used with PureLeaping JumpProblem with a MassActionJump.")
+
+    (; prob, rng) = jump_prob
+    (seed !== nothing) && seed!(rng, seed)
+
+    maj = jump_prob.massaction_jump
+    numjumps = get_num_majumps(maj)
+    rj = jump_prob.regular_jump
+    rate = rj !== nothing ? rj.rate : massaction_rate(maj, numjumps)
+    u0 = copy(prob.u0)
+    tspan = prob.tspan
+    p = prob.p
+
+    if dtmin === nothing
+        dtmin = 1e-10 * one(typeof(tspan[2]))
+    end
+
+    saveat_times, save_start, save_end = _process_saveat(saveat, tspan, save_start, save_end)
+
+    u_current = copy(u0)
+    u_new = similar(u0)
+    t_current = tspan[1]
+    if save_start
+        usave = [copy(u0)]
+        tsave = [tspan[1]]
+    else
+        usave = typeof(u0)[]
+        tsave = typeof(tspan[1])[]
+    end
+    rate_cache = zeros(float(eltype(u0)), numjumps)
+    rate_effective = similar(rate_cache)
+    counts = zero(rate_cache)
+    du = similar(u0)
+    t_end = tspan[2]
+    epsilon = alg.epsilon
+    solver = alg.solver
+    eigenvalue_check = alg.eigenvalue_check
+    stiffness_ratio_threshold = alg.stiffness_ratio_threshold
+    implicit_epsilon_factor = alg.implicit_epsilon_factor
+    numspecies = length(u0)
+
+    nu = zeros(float(eltype(u0)), length(u0), numjumps)
+    for j in 1:numjumps
+        for (spec_idx, stoch) in maj.net_stoch[j]
+            nu[spec_idx, j] = stoch
+        end
+    end
+    reactant_stoch = maj.reactant_stoch
+    hor = compute_hor(reactant_stoch, numjumps)
+    max_hor, max_stoich = precompute_reaction_conditions(
+        reactant_stoch, hor, numspecies, numjumps)
+
+    simple_adaptive_tau_leaping_loop!(
+        prob, alg, u_current, u_new, t_current, t_end, p, rng,
+        rate, nu, hor, max_hor, max_stoich, numjumps, numspecies, epsilon,
+        dtmin, saveat_times, usave, tsave, du, counts, rate_cache, rate_effective, maj,
+        solver, eigenvalue_check, stiffness_ratio_threshold, implicit_epsilon_factor,
+        save_end)
+
+    sol = DiffEqBase.build_solution(prob, alg, tsave, usave,
+        calculate_error = false,
+        interp = DiffEqBase.ConstantInterpolation(tsave, usave))
+    return sol
+end
+
 struct EnsembleGPUKernel{Backend} <: SciMLBase.EnsembleAlgorithm
     backend::Backend
     cpu_offload::Float64