# Scalable Physics-Informed Neural Differential Equations and Data-Driven Algorithms for HVAC Systems

arXiv: https://arxiv.org/abs/2604.18438 · HTML: https://mlsanity.com/paper/2604.18438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 35 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [BubbleNet: Inferring micro-bubble dynamics with semi-physics-informed deep learning](https://mlsanity.com/paper/2105.07179/) (2021)
- [Computational design of antimicrobial active surfaces via automated Bayesian optimization](https://mlsanity.com/paper/2209.00055/) (2022)
- [Eigen-informed NeuralODEs: Dealing with stability and convergence issues of NeuralODEs](https://mlsanity.com/paper/2302.10892/) (2023)

## Abstract (arXiv)

We present a scalable, data-driven simulation framework for large-scale heating, ventilation, and air conditioning (HVAC) systems that couples physics-informed neural ordinary differential equations (PINODEs) with differential-algebraic equation (DAE) solvers. At the component level, we learn heat-exchanger dynamics using an implicit PINODE formulation that predicts conserved quantities (refrigerant mass Mr and internal energy Ehx) as outputs, enabling physics-informed training via automatic differentiation of mass/energy balances. Stable long-horizon prediction is achieved through gradient-stabilized latent evolution with gated architectures and layer normalization. At the system level, we integrate learned components with DAE solvers (IDA and DASSL) that explicitly enforce junction constraints (pressure equilibrium and mass-flow consistency), and we use Bayesian optimization to tune solver parameters for accuracy--efficiency trade-offs. To reduce residual system-level bias, we introduce a lightweight corrector network trained on short trajectory segments. Across dual-compressor and scaled network studies, the proposed approach attains multi-fold speedups over high-fidelity simulation while keeping errors low (MAPE below a few percent) and scales to systems with up to 16 compressor-condenser pairs.