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State-of-the-Art Physics-Based ML for Multimodal Time Series

Research compilation for the movesense physio library. While developed for wearable physiological sensors (ECG + IMU), these architectures are general-purpose: they apply to any domain where multiple synchronized time series encode an underlying physical or dynamical system.

1. State-Space Models (Mamba/S4) for Biosignals

The most active research area for efficient sequence modeling of physiological data.

Paper arXiv Date Key Innovation
ECG-RAMBA: Zero-Shot ECG Generalization 2512.23347 Dec 2025 Bidirectional Mamba with morphology-rhythm disentanglement
BioMamba: Spectro-Temporal Embedding 2503.11741 Mar 2025 Bidirectional Mamba for ECG + EEG, spectro-temporal features
ECGMamba: Efficient ECG with BiSSM 2406.10098 Jun 2024 Bidirectional SSM, lightweight, efficient classification
MambaCapsule: Transparent Cardiac Diagnosis 2407.20893 Jul 2024 Mamba features + capsule networks for interpretability
Chimera: 2D State Space Models 2406.04320 Jun 2024 Extends SSMs to multivariate time series
WildECG: Scaling with SSMs 2309.15292 Sep 2023 Pre-trained SSM on 275K wearable ECG recordings

Best for us: BioMamba or ECGMamba — both are bidirectional SSMs designed for biosignals, efficient enough for MPS.

2. Foundation Models for ECG/Wearable

Pre-trained models that can be fine-tuned for downstream tasks.

Paper arXiv Date Key Innovation
CLEF: Clinically-Guided ECG Foundation 2512.02180 Dec 2025 Contrastive learning with clinical risk scores, single-lead wearable
PhysioWave: Multi-Scale Wavelet-Transformer 2506.10351 Jun 2025 Large-scale pretrained EMG/ECG models with wavelets
NormWear: Multivariate Wearable Foundation 2412.09758 Dec 2024 First multi-modal foundation model for ECG + PPG + ACC
AnyPPG: ECG-Guided PPG Foundation 2511.01747 Nov 2025 100K+ hours, ECG-guided PPG representation

Best for us: NormWear (multi-modal: ECG + ACC) or CLEF (single-lead wearable ECG).

3. Self-Supervised ECG Representation Learning

Learn useful representations without labels from wearable data.

Paper arXiv Date Key Innovation
PLITA: Invariant + Tempo-variant Attributes 2502.21162 Feb 2025 Dual-pathway SSL for single-lead ECG
NERULA: Dual-Pathway Self-Supervised 2405.19348 May 2024 Reconstruction + non-contrastive for single-lead ECG
Self-supervised physiological transfer 2011.12121 Nov 2020 280K hours wrist ACC + ECG, cross-modal SSL

Best for us: PLITA — specifically designed for single-lead ECG SSL.

4. Neural ODEs for Cardiac Dynamics

Paper arXiv Date Key Innovation
Neural State-Space with Causal Disentanglement 2209.12387 Sep 2022 Interacting neural ODEs for cardiac electrical propagation

This area has fewer papers but is highly relevant for physics-informed modeling of cardiac dynamics.

5. Multi-Modal Sensor Fusion

Cross-channel models that combine ECG + ACC + GYRO.

Key approaches from the literature:

  • NormWear (2412.09758): Multi-modal foundation model for wearable sensing
  • Self-supervised transfer (2011.12121): Cross-modal (ACC→ECG) physiological learning
  • Adaptive filtering with IMU reference channels for artifact removal

Implementation Priority

Tier 1 — Implement first (most mature, PyTorch-ready)

  1. ECGMamba / BioMamba: Efficient SSM backbone for ECG classification
  2. CLEF / NormWear: Foundation model fine-tuning for downstream tasks
  3. Self-supervised pre-training: PLITA-style dual-pathway SSL

Tier 2 — Implement next (more specialized)

  1. Neural ODE cardiac dynamics: Physics-constrained latent dynamics
  2. Differentiable DSP: Make bandpass/peak-detection learnable end-to-end
  3. Multi-modal fusion: Joint ECG+ACC+GYRO representation learning

Tier 3 — Research stage (less mature)

  1. PINNs for ECG: Constrained by Einthoven/dipole models — very few papers
  2. Physics-constrained artifact removal: ACC→ECG adaptive filtering with learned components

6. Physics-Informed Architectures (Implemented)

Model arXiv Key Innovation Module
PirateNet 2402.00326 Adaptive residual connections, progressive deepening learned/pinn.py
Physics-GRU 2408.16599 Constrained GRU with smoothness + conservation losses learned/pinn.py
Residual-Based Attention 2509.20349 Attention weighted by physics residual magnitude learned/pinn.py
Symbolic-KAN 2603.23854 Kolmogorov-Arnold Networks with B-spline edges, equation discovery learned/symbolic.py
WARP 2506.01153 Physics-informed linear RNN, 10x better on dynamical systems Referenced

7. Causal Discovery (Implemented)

Method Source Module
Granger Causality (VAR F-test) Classical learned/causal.py
Cross-Channel Causality Discovery Novel learned/causal.py
Transfer Entropy (information-theoretic) Classical learned/causal.py
seq2graph (dynamic dependencies) 1812.04448 Referenced
PCMCI+ (causal time series) tigramite library Referenced

8. Symbolic Regression & Equation Discovery

Paper arXiv Date Key Innovation
Symbolic-KAN 2603.23854 Mar 2026 KAN + symbolic structure for governing equations
LLM-Based Scientific Equation Discovery 2602.10576 Feb 2026 RL-tuned LLMs for symbolic regression
Symbolic Foundation Regressor 2505.21879 May 2025 Pre-trained model for networked dynamical systems
Symplectic Neural Networks 2408.09821 Aug 2024 Hamiltonian dynamics with symbolic regression

9. Why These Models Matter Beyond Wearables

The architectures in this library — PirateNets, PhysicsGRU, KAN, BioSSM, causal discovery, and multi-modal fusion — are not ECG-specific. They are general solutions to a universal problem: learning from multiple synchronized time series governed by underlying physics. Below is a summary of their differential advantages and the breadth of domains they unlock.

Differential Advantages of Each Architecture

Model What It Uniquely Does Why Classical Methods Can't
PirateNet Learns solutions to differential equations while automatically managing network depth. Adaptive residual gates start shallow (stable) and deepen (expressive) during training. Standard PINNs fail with deep networks due to vanishing gradients in PDE residuals. PirateNet solves this without manual architecture tuning.
PhysicsGRU Encodes conservation laws and smoothness priors directly into the recurrent cell. Output can be hard-bounded to physiologically/physically plausible ranges. Standard RNNs have no mechanism to enforce that energy is conserved, mass balances, or outputs stay within physical limits. They learn these implicitly (if at all) from data.
KAN / PhysicsKAN Discovers symbolic governing equations from raw sensor data. Each edge is a learnable B-spline that can be inspected to extract y = f(x) relationships. Neural networks are black boxes. KAN makes the learned function transparent — you can extract F = ma-style equations after training.
ResidualAttention Focuses model capacity on time regions where the physics model is most wrong. Attention weights are proportional to the magnitude of PDE/ODE residual violation. Standard attention treats all time steps equally. This architecture automatically concentrates on anomalies, transients, and model failures — exactly where human experts look.
BioSSM Linear-time sequence modeling (O(N) vs O(N²) for transformers) with selective state spaces. Bidirectional for offline analysis. Handles 100K+ time steps natively. Transformers scale quadratically with sequence length. Hour-long recordings at 200Hz = 720K samples — SSMs handle this; transformers cannot.
Causal Discovery Identifies directed cause→effect relationships between sensor channels (e.g., "motion causes ECG artifact" or "temperature rise precedes pressure drop"). Correlation is not causation. Granger causality and transfer entropy test for directed, time-lagged information flow — essential for understanding why events happen.
MultiModalFusion Cross-modal attention lets each sensor "see" the others. Learns which channels are informative for which events, automatically handling different sampling rates and dimensionalities. Simple concatenation or late fusion ignores the temporal relationships between modalities. Cross-attention captures "when ACC spikes, ECG distorts" patterns.

Downstream Applications by Domain

Healthcare & Clinical

Application Sensors Key Models What's Learned
ICU patient monitoring ECG, SpO2, ABP, respiration, temperature MultiModalFusion + PhysicsGRU Cross-sensor deterioration patterns. PhysicsGRU enforces physiological bounds (HR 30-250, SpO2 0-100%). Causal discovery identifies which vital sign deteriorates first.
Deep brain stimulation (DBS) tuning LFP (local field potentials), EMG, accelerometer, patient diaries BioSSM + CausalDiscovery Real-time detection of pathological oscillations (beta-band in Parkinson's). Causal model links stimulation parameters → tremor reduction → side effects. KAN discovers stimulation→response transfer functions.
Seizure prediction EEG (multi-channel), ECG, ACC BioSSM + ResidualAttention SSM handles long EEG sequences. ResidualAttention focuses on pre-ictal anomalies where the brain's normal dynamics break down.
Anesthesia depth monitoring EEG, EMG, hemodynamics PhysicsGRU + MultiModalFusion Conservation-constrained model of pharmacokinetic drug dynamics. Multi-modal fusion detects awareness events from cross-signal patterns.
Cardiac digital twin 12-lead ECG, echocardiography, CT PirateNet + KAN PirateNet solves cardiac electrophysiology PDEs (bidomain model). KAN extracts patient-specific conduction parameters.

Neuroscience & Behavioral

Application Sensors Key Models What's Learned
Neurobehavioral phenotyping EEG, eye tracking, facial EMG, speech, GSR MultiModalFusion + CausalDiscovery Which neural signals drive which behavioral responses. Transfer entropy quantifies information flow from brain→behavior.
Sleep staging EEG, EOG, EMG, SpO2, respiratory effort BioSSM + ResidualAttention 8-hour recordings at multi-channel. SSM handles the length. ResidualAttention highlights transitions (wake→N1→N2→N3→REM).
Emotion recognition ECG, GSR, respiration, voice, facial video MultiModalFusion + PhysicsGRU Cross-modal attention learns which physiological signals predict which emotional states. PhysicsGRU models autonomic nervous system dynamics.
Cognitive load assessment EEG, pupillometry, typing patterns, HRV CausalDiscovery + KAN Causal model: task difficulty → frontal theta EEG → pupil dilation → HRV change. KAN discovers the quantitative relationship.

Industrial & Engineering

Application Sensors Key Models What's Learned
Predictive maintenance Vibration (ACC), temperature, current, acoustic emission, oil analysis PirateNet + CausalDiscovery + KAN PirateNet learns the machine's nominal dynamics (governing ODEs). Residuals indicate degradation. Causal discovery identifies which sensor predicts failure earliest. KAN extracts remaining-useful-life equations.
Automotive telemetry IMU (6/9-axis), wheel speed, steering angle, brake pressure, GPS MultiModalFusion + PhysicsGRU PhysicsGRU encodes vehicle dynamics (F=ma, tire slip models). Fusion detects anomalous driving patterns. Conservation loss enforces energy/momentum balance.
Structural health monitoring Strain gauges, accelerometers, temperature, humidity PirateNet + ResidualAttention PirateNet learns structural dynamics (wave equation). ResidualAttention focuses on cracks/damage where physics model breaks.
Battery degradation Voltage, current, temperature, impedance spectroscopy PhysicsGRU + KAN PhysicsGRU models electrochemical dynamics with conservation constraints. KAN discovers capacity fade equations.

Environmental & Earth Science

Application Sensors Key Models What's Learned
Seismic event detection Seismometer (3-axis), hydrophone, tiltmeter BioSSM + CausalDiscovery SSM processes continuous seismic streams. Causal discovery links precursor signals across station network.
Climate sensor networks Temperature, humidity, pressure, wind, CO2 MultiModalFusion + PirateNet PirateNet encodes atmospheric dynamics (Navier-Stokes simplified). Fusion handles heterogeneous sensor types and sampling rates.

Audio/Video + Sensor Fusion

Application Sensors Key Models What's Learned
Multimodal speech analysis Audio waveform, laryngeal EMG, airflow, EGG MultiModalFusion + CausalDiscovery Which articulatory gestures cause which acoustic features. Transfer entropy measures speech production→acoustics information flow.
Video + IMU activity recognition Camera (pose estimation), ACC, GYRO MultiModalFusion Cross-modal attention aligns visual pose with inertial measurements. Handles different frame rates (30fps video vs 200Hz IMU).
Surgical robotics Force/torque, video, instrument tracking, tissue imaging PhysicsGRU + ResidualAttention PhysicsGRU models tissue mechanics with force-displacement constraints. ResidualAttention identifies moments where tissue behavior deviates from expected (complications).

The Common Thread

All of these applications share the same structure:

  1. Multiple synchronized time series from different sensor modalities
  2. Underlying physical or biological laws governing the system
  3. Events of interest that manifest as cross-channel patterns
  4. Need for interpretability — not just "what happened" but "why"

The physio library's architecture handles this universally:

Raw multi-modal streams
    → Per-channel encoding (ChannelEncoder / BioSSM)
    → Cross-modal attention (MultiModalFusion)
    → Physics-constrained dynamics (PirateNet / PhysicsGRU)
    → Causal structure (Granger / Transfer Entropy)
    → Symbolic discovery (KAN → governing equations)
    → Events + interpretable explanations

This pipeline is the same whether the input is ECG+ACC from a wearable, vibration+temperature from a turbine, or EEG+EMG from a neuroscience experiment. The physics changes; the architecture doesn't.