1. Enhanced Metamodeling Techniques for High-Dimensional IC Design Estimation Problems Andrew B. Kahng, Bill Lin and Siddhartha Nath VLSI CAD LABORATORY, UC San Diego Presented by: SeokHyeong Kang

2. Outline Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM) Sampling Strategies Low-dimension: NoC High-dimension: PDN-Noise, CTS Conclusions

3. Estimation in IC Design Problems Combinatorial explosion in parameters –Microarchitectural E.g., NoC flit-width, #buffers, #VCs, #Ports –Operational E.g., workload activity factor, supply voltage –Design implementation E.g., core area, tool knobs, constraints –Technology E.g., library, corners –Manufacturing E.g., guardbands

4. Why Surrogate Modeling? Implications of large parameter space – Complex interactions between parameters – Difficult to capture effects in closed-form analytical model Surrogate models can be accurate – Models derived from actual physical implementation data – High accuracy demonstrated in previous works e.g., Samadi10, Nath12

5. Outline Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM) Sampling Strategies Low-dimension: NoC High-dimension: PDN-Noise, CTS Conclusions

6. Axes of Our Studies Modeling techniques – Multivariate Adaptive Regression Splines (MARS) – Radial Basis Functions (RBF) – Kriging (KG) – Hybrid Surrogate Modeling (HSM) Resource Metrics – Number of dimensions (D) – number of samples (N) Sampling strategies – Latin Hypercube Sampling (LHS) – Adaptive Sampling (AS) Quality-of-Results Metrics – Maximum and average percentage errors

7. Our IC Design Estimation Problems Network-on-Chip (NoC) – Estimate: area and power – Dimensionality: low – Parameters: microarchitectural and implementation Power Delivery Network (PDN) – Estimate: cell delay and slew in presence of PDN noise – Dimensionality: high – Parameters: implementation and technology Clock Tree Synthesis (CTS) – Estimate: wirelength and buffer area of clock trees – Dimensionality: high – Parameters: implementation and technology

8. Key Contributions Demonstrate accuracy limits of popular metamodeling techniques as D increases – RBF and KG are preferred at low-D – MARS is preferred at high-D Demonstrate application of Adaptive Sampling (AS) to reduce errors and sample set sizes – Up to 1.5x reduction in worst-case estimation errors – Up to 1.2x reduction in sample set size Present Hybrid Surrogate Modeling (HSM) to achieve up to 3x reduction in worst-case estimation error

9. Outline Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM) Sampling Strategies Low-dimension: NoC High-dimension: PDN-Noise, CTS Conclusions

10. Brief Background on Metamodeling General form of estimation where, Predicted response deterministic response Random noise function Regression coefficients

11. Metamodel Classification Tree-based – MARS Gaussian process-based – RBF – KG We use cross-validation to make models generalizable

12. Regression Function: MARS where, I i : # interactions in the i th basis function b ji : ±1 x v : v th parameter t ji : knot location Knot = value of parameter where line segment changes slope

13. Regression Function: RBF where, a j : coefficients of the kernel function K(.): kernel function µ j : centroid r j : scaling factors

14. Regression Function: KG

15. Outline Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM) Sampling Strategies Low-dimension: NoC High-dimension: PDN-Noise, CTS Conclusions

16. Multicollinearity at High-D

17. Hybrid Surrogate Modeling “Cure” adverse effects of multicollinearity as D increases Variant of Weighted Surrogate Modeling but uses least- squares regression to determine weights where, w 1 : weight of predicted response of surrogate model for MARS w 2 : weight of predicted response of surrogate model for RBF w 3 : weight of predicted response of surrogate model for KG

18. Metamodeling Flow Generate training samples (LHS, AS) Derive model (MARS/RBF/KG/…) Surrogate models Generate test data points Estimate response Compute model accuracy Generate golden data points

19. Outline Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM) Sampling Strategies Low-dimension: NoC High-dimension: PDN-Noise, CTS Conclusions

20. Latin Hypercube Sampling Sample uniformly (“exploration”) across parameter space – Only 5 samples Error

21. Adaptive Sampling Sample using “exploration” and “exploitation” across parameter space – Only 5 samples Error

22. Results of Our PDN Studies AS reduces – error by 1.5x compared to LHS for same #samples – #samples by 1.2x compared to LHS for same % error ~1.5x in error ~1.2x in #samples

23. Outline Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM) Sampling Strategies Low-dimension: NoC High-dimension: PDN-Noise, CTS Conclusions

24. Experimental Setup: NoC (Low-D) Metrics to estimate – Total area of standard cells and total power Parameters – Microarchitectural: # Ports, #VCs, #Buffers, Flit-Width Implementation: Clock frequency Others – Technology libraries: TSMC65GPLUS and TSMC45GS – SP&R Tools: Synopsys Design Compiler and Cadence SOC Encounter – Router RTL: Netmaker from Cambridge University Methodology – Perform SP&R with above tools and parameters – Extract post-P&R area and power – Derive surrogate models

25. Maximum Estimation Error: NoC (Low-D) With a training sample set size of 36 data points – RBF and KG (Gaussian process-based) have in general 1.5x less error than MARS (tree-based) – HSM can have up to 3x less error than MARS RBF, KG and HSM are highly accurate at low-dimensions

26. Outline Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM) Sampling Strategies Low-dimension: NoC High-dimension: PDN-Noise, CTS Conclusions

27. Experimental Setup: PDN (High-D) Metrics to estimate – Cell delay and slew Parameters – Implementation: Cell: cell size, load capacitance, input slew, body bias PDN noise: noise amplitude, noise slew, noise offset Corner: temperature, process-performance ratio – Technology: supply voltage, threshold voltage Others – Technology libraries: TSMC65GPLUS – Tool: Synopsys HSPICE – Netlist: 10-stage INV chain Methodology – Perform SPICE simulation with above parameters – Extract delay and slew of cells – Derive surrogate models

28. Maximum Estimation Error: PDN (High-D) With training sample set size of 700 data points – MARS and HSM have 3x less error than RBF with ridge regression – At D = {8, 9}, MARS and HSM have similar accuracy, because other models have large average errors D = MARS and HSM are highly accurate at high-dimensions

29. Experimental Setup: CTS (High-D) Metrics to estimate – Wirelength and total buffer area Parameters – Implementation: #sinks, buffer type, max. # levels, core area, max. skew, max. delay – Technology: max. buffer size, max. buffer and sink transition times, max. wire widths Others – Technology libraries: TSMC65GPLUS and TSMC45GS – Tool: Cadence SoC Encounter – Testcase: Uniformly placed sinks Methodology – Perform CTS with SOC Encounter and above parameters – Extract wirelength and buffer area of clock trees – Derive surrogate models

30. Maximum Estimation Error: CTS (High-D) With training sample set size of 84 data points – HSM has up to 3x less error than all other surrogate models – Errors grow with D in MARS, RBF, KG due to multicollinearity D = HSM remains highly accurate at high-dimensions

31. Outline Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM) Sampling Strategies Low-dimension: NoC High-dimension: PDN-Noise, CTS Conclusions

32. IC Design Modeling Guidelines All VIF values < 0.33? NY Y Try HSM/RBF/ KG Try MARS N Estimates with small µ & σ 2 ? Try HSM/MARS/RBF/ RBF+RR/KG Try HSM/MARS/ RBF/KG Try MARS D > 5? YN N Y

33. Conclusions Metamodeling techniques can be effective for IC design estimation problems We study three problems along multiple axes – NoC, PDN, CTS – Quality and resource metrics, modeling techniques and sampling strategies We use AS and demonstrate – 1.5x reduction in error vs. LHS – 1.2x reduction in sample size vs. LHS We propose Hybrid Surrogate Modeling (HSM) to “cure” multicollinearity at high dimensions. HSM can be up to 3x more accurate than MARS, RBF and KG at low- and high-dimensions Ongoing: (1) Techniques to reduce multicollinearity, (2) dimensionality reduction, and (3) application to other IC physical design problems

34. Thank you