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+ ModelingToolkit can automatically detect the index and apply appropriate transformations
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+ After index reduction, standard initialization algorithms will work more reliably
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## Performance Tips
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1.**Use `differential_vars` when possible**: This helps initialization algorithms understand problem structure
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2.**Provide good initial guesses**: Even when using automatic initialization, starting closer to the solution helps
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3.**Consider problem-specific initialization**: For complex systems, custom initialization procedures may be more efficient
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4.**Use `CheckInit()` when appropriate**: If you know conditions are consistent, skip unnecessary computation
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1.**Use `differential_vars` when possible**: This helps initialization algorithms understand problem structure
209
+
2.**Provide good initial guesses**: Even when using automatic initialization, starting closer to the solution helps
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3.**Consider problem-specific initialization**: For complex systems, custom initialization procedures may be more efficient
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4.**Use `CheckInit()` when appropriate**: If you know conditions are consistent, skip unnecessary computation
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## References
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- Brown, P. N., Hindmarsh, A. C., & Petzold, L. R. (1998). Consistent initial condition calculation for differential-algebraic systems. SIAM Journal on Scientific Computing, 19(5), 1495-1512.
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- Shampine, L. F. (2002). Consistent initial condition for differential-algebraic systems. SIAM Journal on Scientific Computing, 22(6), 2007-2026.
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- Brown, P. N., Hindmarsh, A. C., & Petzold, L. R. (1998). Consistent initial condition calculation for differential-algebraic systems. SIAM Journal on Scientific Computing, 19(5), 1495-1512.
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- Shampine, L. F. (2002). Consistent initial condition for differential-algebraic systems. SIAM Journal on Scientific Computing, 22(6), 2007-2026.
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