Timesynth: A Temporal Fidelity Framework for Health Signal Digital Twins

Technical Summary: Timesynth: A Temporal Fidelity Framework for Health Signal Digital Twins

Problem Statement
The development of health-signal digital twins—patient-specific computational systems that predict future biological states—relies on forecasting models for physiological time series. However, current evaluation practices suffer from a fundamental gap between forecasting accuracy and physiological fidelity. Standard pointwise metrics, such as Mean Squared Error (MSE) and Mean Absolute Error (MAE), quantify numerical agreement but fail to detect the loss of critical dynamical properties, including oscillatory structure, frequency content, phase relationships, and state transitions.

The authors argue that this limitation creates a "blind spot" where models with comparable pointwise errors may represent the underlying physiological process in drastically different ways. For instance, a model might accurately reproduce signal amplitude while drifting significantly in phase or frequency. Because real clinical recordings lack analytically known ground-truth trajectories for amplitude, frequency, and phase, it is impossible to disentangle these specific error modes in real-world data. Consequently, models may appear reliable by standard benchmarks while failing to preserve the timing and rhythm essential for clinical applications like arrhythmia detection or sleep staging.

Methodology: The TimeSynth Framework
To address this, the authors introduce TimeSynth, a controlled benchmarking framework designed to evaluate the dynamical fidelity of forecasting architectures before they are coupled to patient data. The framework consists of two primary components:

1. Physiologically Grounded Synthetic Generator:

   • Instead of using arbitrary synthetic data, the framework fits closed-form parametric models to real recordings from three public datasets: MIT-BIH Arrhythmia (ECG), PPG-DaLiA (PPG/BVP), and CHB-MIT Scalp EEG (EEG).
   • These parametric models (Drift-Harmonic, Single Phase-Modulated, and Dual Phase-Modulated) generate synthetic time series with analytically known ground-truth for amplitude, instantaneous frequency, and instantaneous phase at every time point.
   • The generator supports controlled perturbations to stress-test models: additive Gaussian noise, frequency distribution shifts, deterministic state transitions, and stochastic Markov switching.

2. Fidelity Diagnostics:

   • Rather than relying solely on aggregate error, TimeSynth employs separate diagnostics to quantify four dimensions of fidelity: Amplitude, Frequency, Phase, and State-Transition preservation.
   • Phase error is calculated via the analytic signal (Hilbert transform), and frequency error is derived from power spectrum peak refinement. State-transition fidelity is assessed using a standardized two-state Gaussian Hidden Markov Model (HMM) probe to measure the recovery of switching statistics via symmetric Kullback-Leibler (KL) divergence.

Experimental Setup
The framework was used to evaluate 11 forecasting architectures spanning four inductive-bias families:

• Linear: Linear, DLinear, FITS.
• MLP-based: MLinear, NBeats, FreMLP.
• Convolutional/Patch-based: MICN (Regre and Mean variants), ModernTCN, PatchTST.
• Full-sequence Attention: Transformer, Autoformer.

Models were tested across five paradigms: clean reconstruction, noise corruption, frequency distribution shift, deterministic state transitions, and stochastic Markov switching.

Key Results
The study reveals a systematic dissociation between pointwise accuracy and dynamical fidelity:

• Pointwise Metrics Mislead: Models with comparable MAE exhibited phase errors differing by up to 53° (approximately 123 ms for a 1.2 Hz cardiac rhythm). Linear and full-sequence attention models often achieved low MAE while losing significant phase and frequency information.
• Locality Preserves Fidelity: Architectures with localized temporal processing (PatchTST, MICN, ModernTCN) consistently preserved oscillatory structure, phase, and frequency under noise and distribution shifts. In contrast, global mappings and full-sequence attention models (Transformer, Autoformer) frequently degraded, particularly under multi-frequency modulation.
• Adaptation Speed: In deterministic state transitions, localized models (PatchTST and ModernTCN) adapted to new states within 6 timesteps (0.6 s at 10 Hz), whereas full-sequence attention models required ~40 timesteps (4 s) to recover, as global attention diffused transition evidence across the context.
• Stochastic Switching Limitation: No architecture reliably preserved stochastic switching dynamics. While PatchTST showed partial recovery in high-probability switching regimes, deterministic point forecasters generally failed to reproduce the transition statistics of the ground truth, suggesting a fundamental limitation of current deterministic approaches for stochastic physiological processes.
• Pareto Analysis: PatchTST emerged as the only model exceeding a normalized score of 0.8 across all five evaluation dimensions (clean, noise, shift, transition, and Markov fidelity), demonstrating the most balanced performance.

Significance and Claims
The paper positions TimeSynth not as a tool to find a single "best" model, but as a principled, use-case-driven framework for model selection and verification. The authors claim:

1. Verification Gap: Current digital twin development lacks frameworks for verifying that predictions preserve physiologically meaningful behavior. TimeSynth provides the "controlled preclinical stress test" required by the National Academies of Sciences, Engineering, and Medicine (NASEM) for verification, validation, and uncertainty quantification (VVUQ).
2. Architectural Determinism: The dominant determinant of fidelity is architectural. The choice of model should be driven by the specific dynamical properties required by the use case (e.g., noise robustness for ambulatory monitoring vs. rapid adaptation for ICU state changes) rather than a search for a universal winner based on aggregate error.
3. Development Infrastructure: TimeSynth offers reusable infrastructure for fidelity-aware development, enabling the generation of controlled ground-truth signals for pretraining and providing interpretable diagnostics to identify which dynamical properties an architecture preserves or destroys.

The authors conclude that while localized temporal processing (specifically PatchTST) currently offers the strongest candidate for health-signal digital twins, the inability of any current architecture to reliably capture stochastic switching indicates a need for future models with explicit latent-state or probabilistic mechanisms.