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partialCBDs: Differentiable Causal Block Diagrams

arXiv 2602.07581 ↗First posted 7 Feb 2026eess.SY cs.LG cs.PLcited by 0

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Abstract (arXiv)

Modern cyber-physical systems (CPS) integrate physics, computation, and learning, demanding modeling frameworks that are simultaneously composable, learnable, and verifiable. Yet existing approaches treat these goals in isolation: causal block diagrams (CBDs) support modular system interconnections but lack differentiability for learning; differentiable programming (DP) enables end-to-end gradient-based optimization but provides limited correctness guarantees; while contract-based verification frameworks remain largely disconnected from data-driven model refinement. To address these limitations, we introduce differentiable causal block diagrams (partialCBDs), a unifying formalism that integrates these three perspectives. Our approach (i) retains the compositional structure and execution semantics of CBDs, (ii) incorporates assume--guarantee (A--G) contracts for modular correctness reasoning, and (iii) introduces residual-based contracts as differentiable, trajectory-level certificates compatible with automatic differentiation (AD), enabling gradient-based optimization and learning. Together, these elements enable a scalable, verifiable, and trainable modeling pipeline that preserves causality and modularity while supporting data-, physics-, and constraint-informed optimization for CPS.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 54 references that are in the map. First posted on arXiv 7 Feb 2026.

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References · 31

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19 more
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