1 / 34

Enhanced Metamodeling Techniques for High-Dimensional IC Design Estimation Problems

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. Outline. Motivation Our Work Metamodeling Background Hybrid Surrogate Modeling (HSM)

candy
Download Presentation

Enhanced Metamodeling Techniques for High-Dimensional IC Design Estimation Problems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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 1.2xreduction 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 modelsgeneralizable

  12. Regression Function: MARS where, Ii : # interactionsin the ith basis function bji: ±1 xv: vth parameter tji: knot location Knot = value of parameter where line segment changes slope

  13. Regression Function: RBF where, aj: coefficients of the kernel function K(.): kernel function µj: centroid rj: scaling factors

  14. Regression Function: KG where, R(.): correlation function (Gaussian, linear, spherical, cubic, …) : correlation function parameter

  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 • If is a linear combination of one or more ’s • Matrix (N x D) of parameters ’s is ill-conditioned • Large variance in ’s • Proper relationship between ’s and is hard to determine • Impact on estimation results • Large errors between and as Dincreases • Diagnostic tests to detect multicollinearity • Variance Inflation Factor (VIF) • F-test • ANOVA

  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, w1: weight of predicted response of surrogate model for MARS w2 : weight of predicted response of surrogate model for RBF w3 : weight of predicted response of surrogate model for KG

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

  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 by1.2xcompared 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 • PDNnoise: 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) 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 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) 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 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 D > 5? N Y All VIF values < 0.33? All VIF values < 0.33? N Y Y N Estimates with small µ & σ2? Y N Try MARS Try HSM/RBF/ KG Try HSM/MARS/RBF/KG Try MARS Try HSM/MARS/RBF/ RBF+RR/KG

  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

More Related