Organizations: School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331 USA · Department of Electrical and Computer Engineering, Yale University, New Haven, CT 06511 USA
Inverse design of RF and electromagnetic (EM) circuits is challenging because the relationship between circuit layout and electrical response is non-unique, and full-wave simulation is computationally expensive. This paper presents K-TRAIL, a simulator-guided generative framework for automated EM/RF circuit synthesis. K-TRAIL combines diffusion-based layout generation with derivative-free ensemble Kalman guidance, allowing feedback from a black-box EM simulator to refine candidate layouts during generation without requiring adjoint sensitivities or differentiable solver models. The framework supports both synthesis from prescribed S-parameter responses and synthesis directly from RF performance constraints. Experiments on multi-layer RFIC structures show that simulator-guided generation improves agreement with target responses and can identify structurally distinct layouts that satisfy circuit-level design requirements. The proposed approach provides a practical path toward generative, verification-aware RF circuit design while retaining the flexibility to explore diverse layout topologies.
Figures & tables
Fig. 1: The proposed Kalman-correction based trajectory refinement for conditional diffusion-based inverse layout generation ( K-TRAIL ) framework supports RF layout generation based on exact S-parameter targets as well as RF constraints
Fig. 2: Multiple layouts with varying degrees of physical realizability and design quality can yield nearly identical scattering responses; inverse design seeks to recover an interpretable and physically realizable layout from a prescribed response.
Fig. 3: Inverse EM/RF design approaches: (a) template-based optimization reduces the search dimension while keeping the outcomes within the solution set of Φ , but restricts the admissible layout space [ 17 , 20 , 23 ] ; (b) free-form optimization expands the design space through structural regularization, which keeps the solutions close to the solution set of Φ [ 12 , 24 ] ; (c) diffusion-posterior methods combine a learned prior with simulator-based response guidance during sampling [ 25 ] ; and (d) direct conditional generative models enable rapid inverse generation, with EM verification performed after sampling [ 26 , 27 ] .
Fig. 4: Sensitivity of electromagnetic response to a small geometric perturbation. For the interleaved layout shown on the left, adding a single metal pixel, indicated by the dashed circle in the right panel, substantially changes the S21 response. This observation underscores a fundamental difficulty in learning EM simulator outputs with standard neural-network surrogates, which often act primarily as interpolative models over the training distribution and may therefore fail to reliably capture sharp response variations caused by small layout modifications.
Fig. 5: Layout templates used to train the diffusion model. From left to right and top to bottom: meandered line, interleaved, coupled line, stub tuner, spiral inductor, and uniform meandered line. A common 500 × 500 μm2 design region and fixed port configurations are used for all topologies.
Fig. 6: Representative simulator-guided synthesis results where y consists of full complex S-parameter values. For each experiment, the layout comparison shows the ground-truth design, the unguided diffusion sample, and the diffusion sample corrected using ensemble Kalman guidance. The corresponding S-parameter responses show that simulator feedback substantially improves agreement with the target response relative to unguided diffusion.
Fig. 7: Representative simulator-guided synthesis results where y consists of only the magnitude of the S-parameter values. For each experiment, the layout comparison shows the ground-truth design, the unguided diffusion sample, and the diffusion sample corrected using ensemble Kalman guidance. The corresponding S-parameter responses show that simulator feedback substantially improves agreement with the target response relative to unguided diffusion.
Fig. 8: Block-level inverse design in which impedance transformation Blocks 1 and 2 are generated using the K-TRAIL approach to satisfy the corresponding block-level constraints. The constraints imposed on the cascaded system are defined in ( 2 ) and illustrated by the shaded regions in the bottom panel.
Fig. 9: Frequency-domain constraint violations for feasible and infeasible responses. A feasible response produces a zero violation vector, whereas a passband dip or stopband leakage produces nonzero components over the affected frequency range.
Fig. 10: Representative two-block design for three experiments. For each experiment, the first row shows the reference and generated block layouts together with the corresponding cascaded S-parameter responses. The constraint margins are shown with dashed green line. The second row compares the reference and generated S-parameter responses for Blocks 1 and 2 individually: (a) Experiment 1, (b) Experiment 2, and (c) Experiment 3.
Fig. 11: Fixed port and lower-layer geometry included in each generated GDS layout.
DoF
Uniform Meander
Nonuniform Meander
Stub Tuner
Interleaved Transformer
Spiral Inductor
Coupled Line
Line Width
1
1
Multiple
1
1
1
Vertical Meander Spacing
1
Multiple
N/A
N/A
N/A
N/A
Horizontal Meander
1
Multiple
N/A
N/A
N/A
N/A
Number of Segments/Stubs
1
1
1
N/A
N/A
N/A
Length
N/A
N/A
Multiple
2
1
Multiple
Trace–Trace Spacing
N/A
N/A
Multiple
1
1
Multiple
TABLE I: Degrees of freedom used to generate the training layouts.