In Situ Learning of Pulse Trajectories

• The paper presents a novel in situ learning framework where pulse trajectories are directly learned and optimized during experiments, bypassing pre-calibration.
• It employs adaptive models like neural state-space models and evolutionary strategies for robust, real-time control in applications ranging from plasma dynamics to ultrafast laser metrology.
• Performance validations show significant improvements in operational fidelity and speed, with error reduction and accelerated calibration across diverse experimental setups.

In situ learning of pulse trajectories refers to the direct, experiment-embedded identification, characterization, and/or control of time-dependent signals (“pulses”) within physical or computational systems. This paradigm forgoes external calibration, pre-characterization, or open-loop modeling in favor of adaptive or data-driven schemes that operate during active operation. Recent work spans applications ranging from plasma dynamics in fusion devices to quantum simulators, photomultiplier detector arrays, and ultrafast laser metrology. Central to the methodology is the real-time or rapidly iterative update of control or inference models from local, experiment-specific data, enabling robust characterization and prediction under dynamic, uncertain, or noisy conditions.

1. Core Principles and System Models

In situ pulse trajectory learning operates on the principle that system dynamics, and their measurement or control, are best learned or calibrated directly within the operational context. Explicit models commonly employ either continuous-time state-space formalisms or parametric representations of pulse shape:

• For plasma control, Wang et al. leverage a neural state-space model (NSSM) of the form $$\dot{x}(t) = f_\theta(x(t), a(t)),\ o(t) = O_\theta(x(t), a(t))$$, embedding physics-guided terms (energy and particle confinement times, power-law scalings) and corrective neural networks (Wang et al., 17 Feb 2025).
• Quantum pulse protocols approximate continuous control by piecewise-constant surrogates (e.g., splitting $[0, T]$ into $L$ intervals and expanding $H(t)$ by average phases $\bar{\phi}_j$), enabling tractable reconstruction and optimization (Dong et al., 2 Dec 2025, Hu et al., 2023).
• For photomultipliers, pulse-shape analysis yields feature vectors capturing amplitude and timing distortions, directly mapped to charge loss by artificial neural networks (Lee et al., 2023).
• Attosecond transient absorption in laser physics extracts instantaneous intensity and phase profiles from delay-dependent spectral signatures (via dipole control and ponderomotive phase modeling) (Blättermann et al., 2016).

2. Algorithms for In Situ Data Acquisition and Model Update

In situ learning frameworks typically employ the following operational cycle:

• Initial Model Training: Using historical or reference data, fit or calibrate the parametric or neural model (e.g., 311 ramp-down pulses in tokamak plasma (Wang et al., 17 Feb 2025), gridwise benchmarking for quantum gates (Hu et al., 2023)).
• Local Experiment Data Integration: After each new operational run (e.g., plasma pulse, quantum algorithm, detector event), append new measurements to the database. For plasma experiments, retraining the NSSM and trajectory optimization completes within $<10$ hours per iteration (Wang et al., 17 Feb 2025).
• Optimization and Policy Update: Employ evolutionary strategies (e.g., OpenAI-ES, CMA-ES) or closed-form signal processing (Magnus expansion, QSP mapping) for trajectory or waveform inference. Reward functions encode system-specific constraints and performance metrics (current/energy targets, chance constraints, gate fidelity, circuit duration).
• Continuous Re-Training: Iterative update cycles incorporate latest measurements, refining models and control policies for robustness against observed or anticipated disturbances.

3. Uncertainty Quantification and Robustness

A distinguishing feature of in situ pulse learning is explicit representation and propagation of uncertainty:

• Plasma rampdown policies are optimized via RL environments sampling from high-dimensional distributions over initial states and model parameters (e.g., H–L mode thresholds, Ohmic heating, radiative losses), guaranteeing policy robustness in $>95\%$ of test scenarios (Wang et al., 17 Feb 2025).
• Quantum pulse protocols incorporate channel noise, SPAM, and depolarizing errors, achieving error bounds $O(1/\sqrt{M})$ for $M$ measured shots and saturating Cramér–Rao lower bounds for phase estimation (Dong et al., 2 Dec 2025).
• Machine learning approaches for pulse restoration rely on observed correlation between shape distortion and charge loss, requiring only a moderate-intensity training set for accurate correction under variable amplitude and saturation (Lee et al., 2023).

4. Methodologies Across Application Domains

The following table summarizes principal in situ pulse learning methodologies across application domains.

Domain	Model/Method	In Situ Data Acquisition
Tokamak Plasma	NSSM + RL + physics priors	Historical + operational rampdowns
Quantum Simulation	QSP phase mapping, CMA-ES	Logical-level propagator queries, LUT
Detector Calibration	ANN shape→charge mapping	Experiment waveforms, cross-calib.
Ultrafast Spectroscopy	DCM phase extraction	Transmission spectra (delay sweep)

Plasma control integrates differentiable ODE simulations (via JAX+diffrax) and RL policy training; quantum learning adopts robust, FFT-based phase inference for pulse reconstruction and evolutionary scheduling for pulse duration/fidelity tradeoffs; detector calibration utilizes waveform-based neural mapping; ultrafast laser metrology employs delay-dependent spectral fitting for extraction of envelope and phase.

5. Quantitative Performance and Validation

Rigorous statistical analysis validates in situ pulse learning effectiveness:

• In plasma rampdown, optimized policies yield statistically significant improvements (Mann–Whitney $p=0.0025$ for $W_{tot}$, $p=0.024$ for $I_p$) over baseline strategies, reducing disruption and rampdown time by $\sim30\%$ (Wang et al., 17 Feb 2025).
• Quantum pulse calibration via QuPAD achieves 15–270× speedup over parameter-shift retraining, with classification accuracy matching simulator benchmarks ($+59.3\%$ over baseline) and VQE energy retrieval within $0.10$ Hartree of ground state (Hu et al., 2023).
• PMT ANN restoration delivers bias $<1\%$ and residuals within $\pm1\%$ over more than an order of magnitude in photoelectron count; RMSE drops from $0.02$ to $<0.005$ for large signals (Lee et al., 2023).
• Ultrafast pulse characterization retrieves pulse envelope width (e.g., $6.9$ fs FWHM) and intensity profile consistent with direct simulation (Blättermann et al., 2016).

6. Workflow Patterns and Iterative Schemes

End-to-end in situ learning workflows follow structured, repeatable patterns:

• Plasma Rampdown: Initialize database, NSSM pre-train, fine-tune to operational regime, loop over run-days with RL-based trajectory optimization, execute shots, append data, retrain, and extrapolate to new scenarios (Wang et al., 17 Feb 2025).
• Quantum Pulse Calibration: Offline circuit parameter regularization, LUT construction, evolutionary dsr search and scheduling, pulse scaling/upload, validation (Hu et al., 2023).
• Waveform-based ANN Correction: Accumulate waveform data with cross-calibration, train ANN on shape→charge mapping, apply to high-intensity runs for live correction (Lee et al., 2023).
• Ultrafast Pulse Retrieval: Acquire spectrogram, fit resonance lineouts to extract phase, model with integrated-sech$^2$ prototype, differentiate for instantaneous intensity (Blättermann et al., 2016).

A plausible implication is that such structured workflows enable rapid “predict–apply–measure–retrain” cycles, with tight coupling of model inference, experimental feedback, and data-driven robustness across physical domains.

7. Generalization and Future Directions

In situ pulse trajectory learning generalizes naturally to systems where temporal control, measurement fidelity, and adaptation to changing conditions are critical. The approach is applicable when:

• Dynamics are highly nonlinear, uncertain, or “unknown unknowns” are prevalent.
• High-precision time-dependent calibration is required but cannot rely on static models or external reference.
• Pulse distortions, noise, or cross-channel interference are context-dependent and not readily precharacterized.

Extensions may include integration of multi-modal measurements, unsupervised or transfer-learning protocols for rare regimes, or fusion of physics-based and data-driven uncertainty propagation. Combined with differentiable programming and real-time optimization, in situ pulse trajectory learning is positioned as a key strategy for robust adaptive control and high-fidelity characterization in next-generation experimental platforms.