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Connor Johnstone
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roadmap/features/12-auto-switching.md
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roadmap/features/12-auto-switching.md
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# Feature: Auto-Switching & Stiffness Detection
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## Overview
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Automatic algorithm switching detects when a problem transitions between stiff and non-stiff regimes and switches to the appropriate solver automatically. This is one of the most powerful features for robust, user-friendly ODE solving.
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**Key Characteristics:**
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- Automatic stiffness detection via eigenvalue estimation
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- Seamless switching between non-stiff and stiff solvers
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- CompositeAlgorithm infrastructure
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- Configurable switching criteria
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- Basis for DefaultODEAlgorithm (solve without specifying algorithm)
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## Why This Feature Matters
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- **User-friendly**: User doesn't need to know if problem is stiff
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- **Robustness**: Handles problems with changing character
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- **Efficiency**: Uses fast explicit methods when possible, switches to implicit when needed
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- **Production-ready**: Essential for general-purpose library
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- **Real problems**: Many problems are "mildly stiff" or transiently stiff
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## Dependencies
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### Required
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- [ ] At least one stiff solver (Rosenbrock23 or FBDF)
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- [ ] At least two non-stiff solvers (have DP5, Tsit5)
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- [ ] BS3 recommended for completeness
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### Recommended
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- [ ] Vern7 for high-accuracy non-stiff
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- [ ] Rodas4 or Rodas5P for high-accuracy stiff
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- [ ] Multiple controllers (PI, PID)
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## Implementation Approach
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### Stiffness Detection
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**Eigenvalue Estimation**:
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```
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ρ = ||δf|| / ||δy||
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```
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Where:
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- δy = y_{n+1} - y_n
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- δf = f(t_{n+1}, y_{n+1}) - f(t_n, y_n)
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- ρ approximates spectral radius of Jacobian
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**Stiffness ratio**:
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```
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S = |ρ * h| / stability_region_size
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```
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If S > tolerance (e.g., 1.0), problem is stiff.
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### Algorithm Switching Logic
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1. **Detect stiffness** every few steps
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2. **Switch condition**: Stiffness detected for N consecutive steps
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3. **Switch back**: Non-stiffness detected for M consecutive steps
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4. **Hysteresis**: N < M to avoid chattering
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Typical values:
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- N = 3-5 (switch to stiff solver)
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- M = 25-50 (switch back to non-stiff)
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### CompositeAlgorithm Structure
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```rust
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pub struct CompositeAlgorithm<NonStiff, Stiff> {
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pub nonstiff_alg: NonStiff,
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pub stiff_alg: Stiff,
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pub choice_function: AutoSwitchCache,
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}
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pub struct AutoSwitchCache {
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pub current_algorithm: AlgorithmChoice,
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pub consecutive_stiff: usize,
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pub consecutive_nonstiff: usize,
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pub switch_to_stiff_threshold: usize,
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pub switch_to_nonstiff_threshold: usize,
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pub stiffness_tolerance: f64,
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}
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pub enum AlgorithmChoice {
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NonStiff,
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Stiff,
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}
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```
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### Implementation Challenges
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1. **State transfer**: When switching, need to transfer state cleanly
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2. **Controller state**: Each algorithm may have different controller state
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3. **Interpolation**: Dense output from previous algorithm
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4. **First step**: Which algorithm to start with?
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## Implementation Tasks
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### Core Infrastructure
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- [ ] Define `CompositeAlgorithm` struct
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- [ ] Generic over two integrator types
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- [ ] Store both algorithms
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- [ ] Store switching logic state
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- [ ] Define `AutoSwitchCache`
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- [ ] Current algorithm choice
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- [ ] Consecutive step counters
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- [ ] Thresholds
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- [ ] Stiffness tolerance
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- [ ] Implement switching logic
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- [ ] Eigenvalue estimation function
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- [ ] Stiffness detection
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- [ ] Decision to switch
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- [ ] Reset counters appropriately
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### Integrator Changes
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- [ ] Modify `Problem` to work with composite algorithms
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- [ ] May need `IntegratorEnum` or dynamic dispatch
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- [ ] Or: make Problem generic and handle in solve loop
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- [ ] State transfer mechanism
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- [ ] Transfer y, t from one integrator to other
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- [ ] Transfer/reset controller state
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- [ ] Clear interpolation data
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- [ ] Solve loop modifications
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- [ ] Check for switch every N steps
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- [ ] Perform switch if needed
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- [ ] Continue with new algorithm
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### Eigenvalue Estimation
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- [ ] Implement basic estimator
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- [ ] Track previous f evaluation
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- [ ] Compute ρ = ||δf|| / ||δy||
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- [ ] Update estimate smoothly (exponential moving average)
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- [ ] Handle edge cases
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- [ ] Very small ||δy||
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- [ ] First step (no history)
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- [ ] After callback event
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### Default Algorithm
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- [ ] `AutoAlgSwitch` function/constructor
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- [ ] Takes tuple of non-stiff algorithms
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- [ ] Takes tuple of stiff algorithms
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- [ ] Returns CompositeAlgorithm
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- [ ] With default switching parameters
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- [ ] `DefaultODEAlgorithm` (future)
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- [ ] Analyzes problem
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- [ ] Selects algorithms based on size, tolerance
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- [ ] Returns configured CompositeAlgorithm
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### Testing
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- [ ] **Transiently stiff problem**
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- [ ] Starts non-stiff, becomes stiff, then non-stiff again
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- [ ] Example: Van der Pol with time-varying μ
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- [ ] Verify switches at right times
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- [ ] Verify solution accuracy throughout
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- [ ] **Always non-stiff problem**
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- [ ] Should never switch to stiff solver
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- [ ] Verify minimal overhead
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- [ ] **Always stiff problem**
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- [ ] Should switch to stiff early
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- [ ] Stay on stiff solver
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- [ ] **Chattering prevention**
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- [ ] Problem near stiffness boundary
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- [ ] Verify doesn't switch back and forth rapidly
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- [ ] Hysteresis should prevent chattering
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- [ ] **State transfer test**
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- [ ] Switch mid-integration
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- [ ] Verify no discontinuity in solution
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- [ ] Interpolation works across switch
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- [ ] **Comparison test**
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- [ ] Run transient stiff problem three ways:
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- [ ] Auto-switching
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- [ ] Non-stiff only (should fail or be very slow)
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- [ ] Stiff only (should work but possibly slower)
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- [ ] Auto-switching should be nearly optimal
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### Benchmarking
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- [ ] ROBER problem (chemistry, transiently stiff)
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- [ ] HIRES problem (atmospheric chemistry)
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- [ ] Compare to manual algorithm selection
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- [ ] Measure switching overhead
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### Documentation
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- [ ] Explain stiffness detection
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- [ ] Document switching thresholds
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- [ ] When auto-switching helps vs hurts
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- [ ] Examples with different problem types
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- [ ] How to configure switching parameters
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## Testing Requirements
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### Transient Stiffness Test
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Van der Pol oscillator with time-varying stiffness:
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```rust
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// μ(t) = 100 for t < 20
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// μ(t) = 1 for 20 <= t < 40
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// μ(t) = 100 for t >= 40
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```
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Expected behavior:
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- Start with non-stiff (or quickly switch to stiff)
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- Switch to non-stiff around t=20
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- Switch back to stiff around t=40
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- Solution remains accurate throughout
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Track:
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- When switches occur
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- Number of switches
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- Total steps with each algorithm
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### ROBER Problem
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Robertson chemical kinetics:
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```
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y1' = -0.04*y1 + 1e4*y2*y3
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y2' = 0.04*y1 - 1e4*y2*y3 - 3e7*y2²
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y3' = 3e7*y2²
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```
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Very stiff initially, becomes less stiff.
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Expected: Should start with (or quickly switch to) stiff solver.
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## References
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1. **Stiffness Detection**:
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- Shampine, L.F. (1977)
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- "Stiffness and Non-stiff Differential Equation Solvers, II"
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- Applied Numerical Mathematics
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2. **Auto-switching Algorithms**:
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- Hairer & Wanner (1996), "Solving ODEs II", Section IV.3
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- Discussion of when to use stiff solvers
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3. **Julia Implementation**:
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- `OrdinaryDiffEq.jl/lib/OrdinaryDiffEqDefault/src/default_alg.jl`
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- `AutoAlgSwitch` and `default_autoswitch` functions
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4. **MATLAB's ode45/ode15s switching**:
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- MATLAB documentation on automatic solver selection
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## Complexity Estimate
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**Effort**: Large (15-25 hours)
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- Composite algorithm infrastructure: 6-8 hours
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- Stiffness detection: 4-6 hours
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- Switching logic and state transfer: 5-8 hours
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- Testing and tuning: 4-6 hours
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**Risk**: Medium-High
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- Complexity in state transfer
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- Getting switching criteria right requires tuning
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- Interaction with controllers needs care
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- Edge cases (callbacks during switch, etc.)
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## Success Criteria
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- [ ] Handles transiently stiff problems automatically
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- [ ] Switches at appropriate times
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- [ ] No chattering between algorithms
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- [ ] Solution accuracy maintained across switches
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- [ ] Overhead < 10% on problems that don't need switching
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- [ ] Performance within 20% of manual optimal selection
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- [ ] Documentation complete with examples
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- [ ] Robust to edge cases
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## Future Enhancements
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- [ ] More sophisticated stiffness detection
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- [ ] Multiple detection methods
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- [ ] Learning from past behavior
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- [ ] Multi-algorithm selection
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- [ ] More than 2 algorithms (low/medium/high accuracy)
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- [ ] Tolerance-based selection
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- [ ] Automatic tolerance selection
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- [ ] Problem analysis at start
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- [ ] Estimate problem size effect
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- [ ] Sparsity detection
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- [ ] Initial algorithm recommendation
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- [ ] DefaultODEAlgorithm with full analysis
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- [ ] Based on problem size, tolerance, mass matrix, etc.
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