Graphene terahertz resonators are often interpreted through conductivity, mobility, or scattering time, whereas device operation is governed more directly by kinetic inductance, resonant-frequency shift, loaded quality factor, and phase. This paper develops a physics-guided neural inversion framework for these device-level quantities and explicitly separates what is supplied to the inverse model from what is inferred. The primary inversion protocol uses the complex resonator spectrum together with calibrated resonator metadata $[\eta _{L},C_{\rm{eff}},L_{g},Q_{e}]$; a spectrum-only protocol is evaluated separately. The independent microscopic and nuisance variables are distinguished from algebraically derived outputs, and a normalized Jacobian singular-value analysis is used to quantify local identifiability. A multi-branch residual spectral-attention network is trained on synthetic responses generated from finite-temperature intraband graphene conductivity, sheet impedance, kinetic inductance, resonator loading, coupling, and measurement noise. Under 40dB test conditions, metadata substantially improves the inversion of $L_{k,\square }$ and $\Delta f_{r}$, while $\tau$ remains weakly identifiable because linewidth changes are partially confounded with contact loss. A metadata-matched nonlinear fit is more accurate for several directly constrained quantities but requires iterative optimization, whereas neural inference is approximately three orders of magnitude faster in the reported implementation. Systematic leave-one-constraint-out ablations show that the physics loss primarily improves algebraic and resonator consistency rather than nominal in-distribution MAE; under an intentionally mismatched complex background and delay, it reduces the mean scaled error by about 25% relative to the data-only network. The results therefore support the method as a fast, calibration-aware inverse engine while explicitly delimiting the parameters that cannot be interpreted as independently identifiable measurements from a single spectrum.
Repeated full-wave evaluations make electromagnetic design expensive, particularly when the physics-based solver is accessed through an interface that does not directly expose response Jacobians. We present a differentiable surrogate method for bounded field-response optimization that separates prediction accuracy from sensitivity reliability. A structured representation combines response transformations with physical and numerical descriptors. Grid-phase features are retained for prediction but detached in the geometry backward path, whose direction and norm are assessed against independent full-wave differences. The resulting sensitivities drive projected updates, followed by full-wave recomputation of frozen candidates. For a three-dimensional metallic cavity, the surrogate achieves test-set relative mean absolute errors of 2.48%-8.65% and $R^{2}>0.95$ across four field metrics. Detachment raises geometry-to-probe RMS cosine agreement from 0.304 to 0.952; waveform-to-probe agreement exceeds 0.998. A gradient-enhanced Kriging comparison evaluates sensitivity fidelity and computational cost, while a dielectricslab benchmark supplies analytical derivative references. A two-port resonator additionally assesses complex S-parameter prediction, sensitivities, and independently verified device optimization. Three-resolution recomputations confirm up to 55.8% probe reduction for fixed-area geometry design and 54.6% selected-probe enhancement with both volume responses reduced by more than 41% for conflicting waveform design. The method enables rapid bounded design while keeping response prediction, sensitivity assessment, and numerical verification independently testable.
We present novel algorithms for automating block placement in Volkov's Block Method to solve the Laplace equation on arbitrary polygonal domains. Although the block method offers exponential convergence through overlapping blocks (sectors of disks, half-disks, and disks)—for boundary data given by algebraic polynomials—its implementation has been limited by the need for manual block placement. Our algorithms automatically generate optimal block coverings, with a theoretical runtime complexity of O(N exp(1/ρ)) for polygons of N sides and an internal parameter ρ. Through head-to-head Pareto comparisons, all implemented in C++ and run on the same machine, against a properly configured hp-adaptive finite-element method (FEM; deal.II), run both with a sparse-direct solver and as a matrix-free method with a multigrid-preconditioned iterative solver, the FreeFEM++ library, the Lightning Laplace solver, and AAA-LS rational approximation, we show that the Block Method attains the best time–accuracy trade-off at high accuracy: at the tightest accuracies it is roughly 13–57x faster than the fastest hp-adaptive FEM variant, while it remains competitive with the Lightning and AAA-LS rational-approximation solvers. We also provide comprehensive benchmarks comparing different block placement strategies and their impact on computational costs and convergence rates. We implement these algorithms in pyBlockMethod, an open-source Python library that integrates seamlessly into scientific workflows for applications in fluid dynamics, electrostatics, heat conduction, and structural analysis. The tool provides an accessible interface to the Block Method while abstracting away block placement.
Hybrid meshing, incorporating combinations of tetrahedral, hexahedral, pyramid, and prism cell shapes, offers enhanced flexibility for electromagnetic simulations. Hybrid meshes also allow multiscale geometries to be treated using conformable meshes. This paper demonstrates the implementation and validation of recently introduced curl-conforming hierarchical and interpolatory basis functions for pyramidal cells with their well-established counterparts for other cell types. Pyramidal elements act as transition cells between regions with different levels of local $h$-refinement, enabling conforming multiscale meshes while preserving high-order continuity across nonuniform discretizations. Numerical results demonstrate high-order accuracy and the absence of spurious modes, thereby validating the robustness and physical fidelity of the proposed approach and confirming the effectiveness of both hierarchical and interpolatory discretizations.
An adjoint-based parallel non-Monte Carlo transient noise analysis method for nonlinear circuits is presented. The proposed approach addresses a key limitation of an existing parallel transient noise framework, namely the cost of solving homogeneous subproblems that constrains scalability with the number of processors available. By solving these subproblems in reverse time using the adjoint method, the proposed method enables their concurrent evaluation on a single processor, thereby significantly reducing the associated computational bottleneck. Consequently, transient noise for a targeted subset of outputs and time points can be computed efficiently without compromising accuracy. Experimental results on nonlinear analog circuits demonstrate up to a threefold speedup over the previous approach.
