Hybrid Dynamical System Modeling and Inference via Machine Learning

Overview

This project tackles the core difficulty of hybrid dynamical systems in power electronics: continuous ODE evolution punctuated by discrete switching events. We design models that (i) explicitly recognize event/mode structure, (ii) embed physics to reduce data burden and preserve interpretability, and (iii) run fast enough at the edge to support control. The result is a practical stack for modeling, inference, and control that remains stable under mode transitions and robust in Sim-to-Real deployment.

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Why This Research

• Hybrid dynamics are hard to learn. Standard discrete networks conflate sampling with dynamics and struggle with irregular mode durations.
• Sim-to-Real is brittle. Pure physics breaks under parameter drift; pure black-box needs huge data and often fails at mode boundaries.
• Edge devices are resource-constrained. Real-time requirements (sub-µs) and tight memory make classic high-order solvers impractical.
• Goal. Build event-aware, physics-consistent, edge-deployable models that keep continuous-time fidelity, cross mode transitions cleanly, and meet hard latency budgets.

New Measures

• Event-Automata Learning (EA). Decode control/PWM into mode sequences and event times, then learn per-mode dynamics; avoids sampling delay and reduces learning interference across modes.
• Physics-Embedded Neural ODEs (PENODE). Parameterize the continuous-time vector field as f(x,u)=f_phy(x,u;θ_phy)+f_NN(x;θ_NN). Physics supplies a stable backbone; the NN learns residuals only—improving data efficiency, interpretability, and generalization.
• Neural Substitute Solver (NSS). Replace two bottlenecks in numerical solvers with lightweight NNs: (1) event-triggered model updates (matrix ops) and (2) higher-order truncation terms of the integrator—turning sequential steps into parallel forward passes suitable for FPGA/MPSoC.
• Unified training with adjoint/backprop. Jointly optimize physical parameters and NN weights end-to-end; supports white-, gray-, and black-box regimes with a single pipeline.
• Cloud→Edge toolchain. Quantization-aware training, operator fusion, and HLS-based accelerators map PENODE/NSS to FPGAs/MPSoCs with deterministic timing; EA provides event-driven scheduling at inference.
• Data program for Sim-to-Real. Curate mixed simulation + hardware traces across modes and operating ranges; use EA to segment/align trajectories, then fine-tune to the target plant with small data.

Impact

• Learning efficiency. Event-aware decomposition reduces model size and accelerates convergence compared with single-mode discrete nets; residual learning lowers data demand.
• Sim-to-Real reliability. Physics-anchored representations maintain accuracy under parameter drift and unseen conditions; unified training avoids two-stage inconsistencies.
• Real-time edge inference. NSS and compact PENODE kernels deliver consistent per-step latency with low resource use—suitable for sub-µs budgets.
• Control integration. Continuous-time states/derivatives and clean mode boundaries feed MPC/optimal control without ad-hoc filters; improved transients and stability margins.
• Maintainability & insight. Physical parameters remain visible and tunable; residual terms highlight unmodeled effects for diagnostics.

Publications