# Adjoint method

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arXiv Nov 12, 2026
A financial diffusion sampler gets a new time grid: TAPES posts the lowest paired error in all 24 rows, cutting audit error about 10%
Financial scenario pipelines often run diffusion samplers at very few function evaluations, where time-grid discretization error can quietly distort terminal reports such as covariances, tails and drawdown proxies. TAPES treats grid construction as a goal-oriented numerical problem: Richardson comparisons estimate each step's signed local defect, a terminal-report adjoint transports those defects through the remaining discrete flow, and the squared norm of their sum is minimized before a capped direct refinement. Across six budgets on Regime-SV and Mag7, TAPES gives the lowest design- and audit-report errors in all 24 dataset–budget–report rows within the reported five-pipeline panel, with cross-budget mean relative audit-error reductions of about 10–11% and about 1%.
Financial scenario pipelines often run diffusion samplers at very few function evaluations, where time-grid discretization error can quietly distort terminal reports such as covariances, tails and drawdown proxies. TAPES treats grid construction as a goal-oriented numerical problem: Richardson comparisons estimate each step's signed local defect, a terminal-report adjoint transports those defects through the remaining discrete flow, and the squared norm of their sum is minimized before a capped direct refinement. Across six budgets on Regime-SV and Mag7, TAPES gives the lowest design- and audit-report errors in all 24 dataset–budget–report rows within the reported five-pipeline panel, with cross-budget mean relative audit-error reductions of about 10–11% and about 1%.
Yilie Huang（First author, Corresponding author）
TAPES Timestep Scheduling Adjoint method Score-Based Diffusion Sampling
arXiv Nov 9, 2026
Plasma feedback control drops full phase-space sensing: macroscopic currents and field gradients alone hold instabilities down under substantial delay
For kinetic plasmas governed by the Vlasov–Maxwell system, feedback control has either taken the full phase-space perturbation as input or relied on instantaneous field cancellation, which degrades once sensing and actuation delays appear. This controller instead uses macroscopic quantities such as current densities, electromagnetic fields and their spatial gradients as feedback information, and a low-rank neural operator learns a residual correction to the delayed cancellation baseline while the control objective stays kinetic: stabilizing the full distribution toward a prescribed equilibrium. In numerical experiments on two-stream and Weibel-type current-filamentation instabilities, the controller keeps suppressing perturbation growth over long times under substantial feedback delay.
For kinetic plasmas governed by the Vlasov–Maxwell system, feedback control has either taken the full phase-space perturbation as input or relied on instantaneous field cancellation, which degrades once sensing and actuation delays appear. This controller instead uses macroscopic quantities such as current densities, electromagnetic fields and their spatial gradients as feedback information, and a low-rank neural operator learns a residual correction to the delayed cancellation baseline while the control objective stays kinetic: stabilizing the full distribution toward a prescribed equilibrium. In numerical experiments on two-stream and Weibel-type current-filamentation instabilities, the controller keeps suppressing perturbation growth over long times under substantial feedback delay.
Jingcheng Lu（First author）
Optimal Control Operator Learning Adjoint method Plasma Instability Suppression
arXiv Oct 8, 2026
Three-sensor machine-learning phase-amplitude reduction speeds airfoil wake synchronization eightfold while curbing lift fluctuations
This study combines phase-amplitude reduction with nonlinear machine-learning sparse-sensor reconstruction to estimate phase and amplitude sensitivity fields from only three airfoil-surface sensors and analytically derive optimal actuation waveforms for fast synchronization of post-stall airfoil wake shedding; the identified optimal forcing alters wake frequency eight times faster than standard sinusoidal actuation, and the amplitude-penalized waveform suppresses lift-coefficient fluctuation relative to the optimal forcing without amplitude penalty.
This study combines phase-amplitude reduction with nonlinear machine-learning sparse-sensor reconstruction to estimate phase and amplitude sensitivity fields from only three airfoil-surface sensors and analytically derive optimal actuation waveforms for fast synchronization of post-stall airfoil wake shedding; the identified optimal forcing alters wake frequency eight times faster than standard sinusoidal actuation, and the amplitude-penalized waveform suppresses lift-coefficient fluctuation relative to the optimal forcing without amplitude penalty.
Johns Hopkins University Tohoku University Institute of Science Tokyo
Daiki Beppu（First author）
Phase-amplitude reduction Machine-learning-based sparse sensor reconstruction Fast synchronization of airfoil wakes Sparse Identification of Nonlinear Dynamics Adjoint method

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A financial diffusion sampler gets a new time grid: TAPES posts the lowest paired error in all 24 rows, cutting audit error about 10%

Plasma feedback control drops full phase-space sensing: macroscopic currents and field gradients alone hold instabilities down under substantial delay

Three-sensor machine-learning phase-amplitude reduction speeds airfoil wake synchronization eightfold while curbing lift fluctuations