End-to-End Neural Modeling of EM Response and Design Performance for Free-Form RFIC Passives

1 Introduction

• Prior neural methods often restrict layouts, omit downstream design-performance modeling, or lack explicit circuit conditioning and broad, flexible frequency coverage.The introduction identifies these gaps as motivation for end-to-end modeling of free-form passives within surrounding circuit contexts.Source: §1 · pp. 1–2
• The paper uses “network” to mean a passive matching network rather than a neural network, unless stated otherwise.The introduction considers these passives within surrounding circuit contexts, such as auxiliary capacitors.Source: §1 · pp. 1–2
• The proposed framework pairs a frequency-conditioned neural simulator with a circuit-conditioned solver to predict EM response and design performance under varying settings.Its neural EM response combines explicit and complementary responses; a dependence regularizer encourages independence between them.Source: §1 · p. 2
• The study constructs a large-scale free-form passive dataset from expert-designed contours and random paths.The dataset supports a comprehensive empirical study of the proposed framework.Source: §1 · p. 2
• R2 > 0.98 for almost all targets; the 21M-parameter model evaluates orders of magnitude faster than traditional EM simulation, which can take up to 20 minutes per full-frequency evaluation.On an RTX 2080 Ti, the simulator runs at 121 full-frequency simulations per second and the solver at 25,069 full-frequency predictions per second.Source: §1 · p. 2

2 Background

• A typical PA uses passive matching networks at its input, between stages, and at its output.These small on-chip passive circuits reshape how RF signals pass between blocks.Source: §2 · p. 2, Figure 2 · p. 3
• The modeled symmetric layouts use two metal layers on a fixed 18 × 18 pixel grid, with circuit context parameterized by capacitors C1 and C2.The structures are reciprocal, with ports mutually connected; the three matching placements are modeled separately.Source: §2 · p. 3
• Targets include frequency-dependent complex S-parameters, complex input impedance Zin, passive efficiency, and max gain.The full S-matrix has shape 8 × 8; reciprocity and layout symmetry reduce it to 20 distinct complex entries.Source: §2 · p. 3
• Traditional evaluation runs a finite-difference EM simulator over frequency, then embeds its response in the circuit for downstream performance evaluation.A full-frequency EM evaluation can require up to 20 minutes, slowing iterative design and large-scale exploration.Source: §2 · p. 3

Problem Formulation

• The free-form layouts use pixel-based geometry on a fixed grid and include contour-seeded masks near expert designs and RandPath-seeded connected layouts.The masks are symmetric and represented on a 2 × 18 × 18 grid; each layout is evaluated across sampled circuit contexts and a frequency grid.Source: §3 · p. 3

Overview

• The simulator maps layout and frequency to explicit EM and complementary responses, which the circuit-conditioned solver combines with circuit context to predict design performance.The complementary response preserves information useful for design prediction when the explicit EM response is imperfect.Source: §3 · p. 4, Figure 4 · p. 4

Frequency-Conditioned Neural Simulator

• Frequency conditioning modulates the shared layout backbone through learned, position-specific scale and shift parameters across four residual blocks.A Fourier frequency encoding with K=10 captures low- and high-frequency variation, and the modulation parameters can be cached across layouts at a given frequency.Source: §3 · pp. 4–5

Circuit-Conditioned Neural Solver

• The solver Fourier-encodes C1 and C2, concatenates their embeddings with the neural EM response, and uses an MLP to predict design performance.This allows the solver to use both the predicted EM response and circuit context.Source: §3 · pp. 4–5

Robustness

• The learned solver can adapt to errors in the neural EM response, enabling design-performance prediction despite imperfect EM predictions.The cited discussion contrasts this with the high sensitivity of a ground-truth downstream solver to perturbations in its EM-response input.Source: §3 · p. 5

Joint Training Objective

• The simulator and solver are trained jointly with normalized mean-squared-error losses for EM response and design performance.The joint supervision keeps the simulator faithful to the EM target while encouraging representations useful for downstream prediction.Source: §3 · p. 5

Dependence Regularization

• The dependence regularizer reduces correlation between the complementary response and predicted EM response, applying its constraint only to the complementary response.The paper reports substantially reduced interdependence with little loss in accuracy.Source: §3 · pp. 5–6

Experimental Details

• The 61,515-layout dataset is split 7:1:2 into training, validation, and test sets, and multi-dimensional targets are scored by averaging R² across dimensions.For example, the paper reports average R² when a target has multiple dimensions.Source: §4 · p. 6
• Models use fixed hyperparameters across scales and matching settings, and each reported result comes from a single end-to-end run despite high compute cost.The authors report that results are stable across model scales and matching settings in independent runs.Source: §4 · p. 6

Interpolation Between Training Frequencies

• The 21M input-matching model interpolates smoothly at unseen frequencies within the 10–60 GHz training band, though high-frequency responses appear less smooth.The evaluation queries a 100× denser grid at 0.001 GHz spacing; extrapolation is not evaluated.Source: §4 · p. 6, Figure 5 · p. 7

Main Results Across Model Scales and Matching Settings

• Scaling from 5.4M to 21M parameters improves EM-response and design-performance R² across input, interstage, and output matching settings.The comparison covers the full distribution and its two constituent distributions.Source: §4 · p. 6, Table 2 · p. 7

Per-Target Accuracy Across Frequency

• Scaling to 21M improves all input-matching targets across frequency, with the clearest gains in difficult regimes; max gain remains the hardest target, about 10% below the others.Figure 6 compares per-target R² over frequency for the 21M and 5.4M models.Source: §4 · p. 7, Figure 6 · p. 8

Training Compute and Dataset Scaling

• Longer training and larger RandPath-seeded training subsets improve accuracy, with the largest gains on challenging targets with lower R².The data-scaling comparison uses a fixed training budget equivalent to 50 full-data epochs.Source: §4 · p. 7, Figure 8 · p. 9

Effect of the Complementary Response

• Adding the complementary response improves average R² for every target, with the largest gain on high-frequency |S| and protection against low-frequency degradation in |Zin| and its phase.The remaining targets also receive consistent gains across the frequency band.Source: §4 · pp. 7–8

Effect of Dependence Regularization

• Dependence regularization reduces Corr(Ŝ, Zcomp) from 0.149 to 0.006, a 96% reduction, while design R² changes only from 0.967 to 0.964.The reported result characterizes a cleaner decomposition while preserving design-performance accuracy.Source: §4 · p. 9

Limitations

• Cross-family accuracy remains below in-distribution accuracy, and the evidence does not establish generalization beyond the two layout-generation families.The study uses a fixed 18 × 18 grid, two metal layers, and separate models for input, interstage, and output matching.Source: §5 · p. 9
• Current checkpoints are not expected to transfer to different layout resolutions or process technologies without adaptation or retraining.Dense-frequency evaluation demonstrates interpolation within the training band rather than extrapolation beyond it.Source: §5 · p. 9
• Training is expensive, particularly for the 21M model, and the study does not quantify variability across random seeds.Source: §5 · pp. 9–10

Additional Frequency-Dependent Analyses

• Figure 10 analyzes generalization between Contour-seeded and RandPath-seeded families, while Figure 11 reports average correlation for dependence regularization.Source: Figure 10 · p. 10, Figure 11 · p. 10

Limitations

• Predicted EM responses do not guarantee physical properties such as passivity, although better models show lower passivity-violation rates.Source: §5 · p. 10

Future Work

• Future work proposes variable-size layouts, further scaling, and conditioning on properties such as material effects.Variable-length patch-token sequences are suggested to relax the fixed-size layout constraint.Source: §5 · p. 10
• Stronger transfer from RandPath-seeded than Contour-seeded training motivates broader randomized training-distribution coverage.The paper recommends prioritizing randomized simulation data for broad free-form generalization over exclusive reliance on template-seeded layouts or predefined transformer families.Source: §5 · p. 10

• The 21M model achieves high accuracy across input, interstage, and output matching settings while evaluating orders of magnitude faster than traditional EM simulation.The conclusion frames these results as suggesting faster RFIC passive design-space exploration, with future extensions toward more diverse layouts, flexible dimensions, and broader circuit settings.Source: §6 · p. 10

LLM Disclosure

• PIRA assisted with implementation aids and writing polishes; the authors are responsible for the final content.Source: LLM Disclosure · p. 11

A Related Work

• Related neural surrogates primarily accelerate EM-response evaluation, whereas this framework jointly predicts explicit EM response and downstream performance for free-form PA matching networks.Source: A Related Work · p. 13
• Related neural design methods extend to inverse design and automated flows, but mainly optimize or synthesize structures through EM-response targets or design-flow validation.Source: A Related Work · p. 13

B Additional Frequency-Dependent Analyses

• Additional frequency-dependent analyses cover scaling, training evolution, dense-frequency queries, and dependence regularization for interstage and output matching.Source: B Additional Frequency-Dependent… · p. 13

B.1 Frequency-Level Scaling Analysis

• For interstage matching on the full distribution, Figure 12 plots per-target R2 over frequency for the 21M and 5.4M models.Source: Figure 12 · p. 14
• For output matching on the full distribution, Figure 13 plots per-target R2 over frequency for the 21M and 5.4M models.Source: Figure 13 · p. 14

B.2 Frequency-Level Training Analysis

• For interstage matching on the full distribution, Figure 14 plots per-target R2 over frequency across training epochs for the 5.4M model.Source: Figure 14 · p. 15
• For output matching on the full distribution, Figure 15 plots per-target R2 over frequency across training epochs for the 5.4M model.Source: Figure 15 · p. 15

B.3 Dense-Frequency Query Analysis

• Interstage matching predictions are shown on a 0.001 GHz grid, 100× denser than the training grid.The figure covers dense-frequency queries for the 21M model.Source: Figure 16 · p. 16
• Output matching predictions are shown on a 0.001 GHz grid, 100× denser than the training grid.The figure covers dense-frequency queries for the 21M model.Source: Figure 17 · p. 16

B.4 Dependence-Regularization Frequency Analysis

• Per-target R2 over frequency is plotted for the 21M input matching model under different dependence-regularization strengths on the full distribution.Source: Figure 18 · p. 17

C Sensitivity to the Simulator Backbone

• The comparison replaces the residual backbone with a shallow CNN of comparable parameter count, retaining frequency conditioning and the neural solver.Both models were trained for 100 epochs on the full mixed-distribution input-matching training split.Source: C Sensitivity to the Simulator Backbone · p. 17
• The CNN’s R2 design is lower by 0.00258, with maximum-gain R2 of 0.86045 versus 0.87938 for the residual model.Table 3 compares the simulator backbones after 100 training epochs.Source: C Sensitivity to the Simulator Backbone · p. 17, Table 3 · p. 17
• The CNN achieves slightly higher R2 EM, while the two backbones have comparable aggregate accuracy.Source: C Sensitivity to the Simulator Backbone · p. 17

D Physical Consistency of Predicted EM Responses

• Passivity is counted when the largest singular value of the reconstructed S matrix exceeds 1 + 10^-6, across 501,000 layout–frequency pairs.The evaluation samples 1,000 test layouts and tests all 501 frequencies for each layout.Source: D Physical Consistency of Predicted EM… · p. 17
• The 21M model has passivity-violation rates below 7% in every matching setting, but neither model guarantees passivity.Ground-truth responses on the same sample have a 0.138% violation rate under the same criterion.Source: D Physical Consistency of Predicted EM… · pp. 17–18

E Solver-Stability Evaluation Protocol

• The solver-stability experiment tests how small input-response errors propagate to design-performance predictions in input matching.Source: E Solver-Stability Evaluation Protocol · p. 18

E.1 Noise Injection and Solver Evaluation

• The ground-truth solver receives independently noised ground-truth EM responses, with noise from 1% to 20% of each dimension’s empirical standard deviation and a noiseless reference.Frequency and circuit context are held unchanged.Source: §E.1 · p. 18
• The learned solver is evaluated with the same dimensionwise noise rule applied to its predicted neural EM response, including both explicit and complementary responses.The trained solver, frequency, and circuit context remain fixed; predictions are compared with ground-truth design targets using R2 design.Source: §E.1 · p. 18

E.2 Magnitude and Effect of EM Simulation Response Noise

• The added noise changes the sampled S-parameter values only slightly, while the ground-truth solver’s design-performance R2 is already negative at 4%.Table 5 presents the first complex S-parameter entry for three sampled examples before and after perturbation.Source: §E.2 · p. 18, Table 5 · p. 18
• At 4% noise, the ground-truth solver’s design-performance R2 becomes negative, while the learned solver retains R2 design = 0.9808 versus 0.9814 without added noise.The perturbed EM responses retain aggregate R2 EM of 0.9984.Source: §E.2 · p. 18
• The learned solver’s accuracy decreases gradually as noise increases; no artificial response noise was injected during training, and the behavior may emerge from joint training.The authors suggest exposure to imperfect simulator predictions as a possible reason.Source: §E.2 · p. 19

NeurIPS Paper Checklist

• The paper lists fixed-grid, process-specific evaluation, separate models by matching placement, limited cross-distribution generalization, interpolation-only frequency evaluation, training cost, unquantified seed variability, and lack of guaranteed passivity as limitations.Source: NeurIPS Paper Checklist · p. 20
• The dataset cannot be publicly released because of commercial licensing constraints, although construction details and code are provided to support reproduction.Source: NeurIPS Paper Checklist · pp. 21–22
• Main predictive-performance results come from single training runs, and variability across random seeds is not quantified.The reported passivity-rate error bars do not measure seed variability or account for within-layout frequency dependence.Source: NeurIPS Paper Checklist · p. 23