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This message introduces an open-source analytical solver for dynamic thermal simulation and Model Predictive Control (MPC) architectures.</div>
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Large-scale stochastic optimization and sub-hourly MPC encounter structural bottlenecks: the computational cost of spatial discretization (FDM) and the numerical instability of standard Transfer Matrix Methods (TMM) under high-frequency transient forcing. Standard
state-space models also systematically assume material homogeneity, truncating hygrothermal degradation.</div>
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A frequency-domain framework based on the continuous spatial Riccati equation has been published to bypass these limits.</div>
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Applied capabilities:</div>
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<div class="elementToProof" role="presentation">Moisture-driven degradation: The framework analytically integrates continuous spatial property gradients (¥ë(x)) via perturbation theory. For wetted porous media, it captures unaccounted peak heating loads (correcting
a 21.9% deviation in wetted AAC envelopes) without requiring internal nodal meshing.</div>
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<div role="presentation">Non-linear boundary conditions: It isolates Stefan-Boltzmann radiative exchanges (T©ù) as harmonic source terms to model nocturnal subcooling under clear skies, correcting the heat discharge overestimations produced by linearized LTI
coefficients.</div>
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<div role="presentation">Algorithmic stability: By algebraically bounding positive exponential wave arguments, the solver eliminates high-frequency overflow crashes. The single-step macroscopic integration executes in 0.02 ms, enabling multi-week time-domain
reconstructions for parametric runs or real-time MPC dispatch.</div>
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The formal mathematical derivation, physical benchmarks, and error bounding are detailed in the published article (
<a href="https://doi.org/10.1080/19401493.2026.2657578" id="OWAd65b7cbc-e4ee-cc4c-74b9-e236f705248b" class="OWAAutoLink">
https://doi.org/10.1080/19401493.2026.2657578</a> ) and its open-access preprint (
<a href="https://hal.science/hal-05602751" id="OWA2c3bf7d7-1d17-c4bd-f1a5-07fb28334c4c" class="OWAAutoLink">
https://hal.science/hal-05602751</a> ).</div>
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The Python source code is available for direct integration on Zenodo: <a href="https://doi.org/10.5281/zenodo.19783248">
https://doi.org/10.5281/zenodo.19783248</a> </div>
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Corentin Guigot</div>
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Associate Professor</div>
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CESI LINEACT</div>
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