Neural Parameter Estimation of RC Thermal Building Models for Model Predictive Control

Fabian Raisch; Timo Germann; Sang-Woo Ham; J. Nathan Kutz; Christoph Goebel; Benjamin Tischler

eess.SYApr 7, 2026

Neural Parameter Estimation of RC Thermal Building Models for Model Predictive Control

Authors: Fabian Raisch, Timo Germann, Sang-Woo Ham, J. Nathan Kutz, Christoph Goebel, Benjamin Tischler

Organizations: Technical University of Applied Sciences Rosenheim, Rosenheim, Germany · Technical University of Munich, Munich, Germany · Ludwig Maximilian University of Munich, Munich, Germany · Lawrence Berkeley National Laboratory, Berkeley, USA ·

Abstract

Gray-box RC models are widely used to enable energy-efficient model predictive control (MPC) in buildings. However, estimating RC parameters remains difficult, as conventional optimization-based algorithms are prone to local minima, rely heavily on good initial guesses, and incur high computational cost. To address these issues, we propose the Estimator from Scratch, a novel neural parameter estimation approach that embeds the physical equations into a neural network's training process to estimate RC parameters. To further improve estimation accuracy and eliminate dependence on an initial guess, we extend this approach by pretraining the neural network on data from multiple source buildings, the Pretrained Estimator. We benchmark both methods against a genetic-algorithm-based RC estimator and a fully black-box neural network. All methods are evaluated across eight simulated and three real-world buildings for two RC configurations, for both prediction accuracy and closed-loop MPC performance, the latter only for the simulated buildings. The Pretrained Estimator achieves the best prediction performance among all RC-based methods, particularly with little training data, and yields the lowest and least variable MPC costs across buildings and benchmarks. These results position the Pretrained Estimator as a robust, computationally efficient, and initial-guess-free alternative for RC parameter estimation, with potential to extend to other control-oriented dynamical systems.

Figures & tables

Figure 1. Considered RC circuits defining

{d\mathbf{x}}/{dt}=f_{\bm{\theta}}(\mathbf{x},\mathbf{u},\mathbf{d})

Figure 2. Concept of neural parameter estimation for control-oriented systems. A neural network maps training examples sliced from measurement data to parameter estimates

\hat{\bm{\theta}}^{j}

. These estimates are used to parameterize a chosen RC model, which is then simulated to calculate the loss for the neural network update.

Parameter	Lookback	Layers	Neurons per layer	Output size	Input size
Selected	96	2	140	$n\times 1$	$96\times 4$

Table 1. Hyperparameter selection for the MLP of the Estimator from Scratch and the Pretrained Estimator.

Parameter	Unit	Sources
$U_{wall}$	$[W/m^{2}K]$	$\{0.1,0.4,0.7,1,1.3\}$
$c_{wall}$	$[kJ/m^{2}K]$	$\{30,165,300\}$
$f_{win}$	-	$\{0.15,0.20\}$
$A_{ground}$	$[m^{2}]$	$\{60,90,120\}$
Weather	-	Belgrade, Prague, Berlin, London, Zurich

Table 2. Distribution of physical properties for the source buildings, from ( Raisch et al., 2025 ) : insulation U-value (

U_{wall}

), area-specific heat capacity (

c_{wall}

), window-to-wall ratio (

f_{win}

), and ground area (

A_{ground}

) with the remaining building properties calculated from these values ( Krug et al., 2026 ) .

Target building	$U_{wall}$ $[W/(m^{2}K)]$	$c_{wall}$ $[kJ/(m^{2}K)]$	$f_{win}$	$A_{ground}$ $[m^{2}]$	$T_{sp,\,day}$ [°C]	$\Delta T_{night}$ [°C]	Weather
T1	0.25	280	0.19	100	21.0	2.0	Amsterdam
T2	0.25	40	0.16	70	22.0	1.0	Bratislava
T3	0.55	150	0.16	70	23.0	3.0	Amsterdam
T4	0.55	280	0.19	100	20.5	1.5	Munich
T5	0.85	150	0.19	100	22.5	0.5	Bratislava
T6	0.85	40	0.16	70	22.0	2.5	Munich

Table 3. Properties of target buildings ( Raisch et al., 2025 ) with the daytime setpoint

T_{sp,\,day}

and a potential night setback

\Delta T_{night}

Figure 3. Setup for variable training lengths. The test set remains fixed.

Time	$T^{\text{low}}$	$T^{\text{up}}$
Mon.–Fri. 6:00–18:00	17 $\mathrm{\SIUnitSymbolCelsius}$	24 $\mathrm{\SIUnitSymbolCelsius}$
Mon.–Fri. 18:00–6:00	20 $\mathrm{\SIUnitSymbolCelsius}$	21 $\mathrm{\SIUnitSymbolCelsius}$
Sat.–Sun.	20 $\mathrm{\SIUnitSymbolCelsius}$	21 $\mathrm{\SIUnitSymbolCelsius}$

Table 4. Comfort range for the indoor temperature.

Figure 4. RMSE and NRMSE (in K) for the 2R2C model with 12 days of training data, shown as paired scatter plots for the simulated and real-world buildings. For GA, the NRMSE value of 4.60 is omitted for visual clarity.

Figure 5. Average (full color) and min-max (dashed, light color) RMSE values in K for simulated and real-world buildings as a function of training data length for the 2R2C, 1R1C, and the MLP benchmark.

Figure 6. Total MPC cost (logarithmic scale) for all methods averaged (bar) and shown as scatter per building (T1–T8).

Method	T1	T2	T3	T4	T5	T6	T7	T8
GA	155	594	133	142	126	170	145	154
PE	141	413	147	139	124	159	142	147
Scratch	138	440	304	146	125	160	144	149
PI contr.	202	477	178	200	231	206	454	171
MLP	5571	7729	999	3617	2823	3141	2428	17714

Table 5. Total cost by method and building. Best (lowest) total cost per building in bold, second-best underlined.

Figure 7. Resulting indoor temperature and control signal for building T2 for the first days of the MPC test period, with ambient temperature and solar irradiation shown as disturbances.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 8. RMSE values in K as a function of training data length for the 2R2C and 1R1C models, shown for the real buildings.

Figure 9. RMSE values in K as a function of training data length for the 2R2C and 1R1C models, shown for simulated buildings.

Figure 10. Heating activity vs. thermal discomfort per building and method (both axes log-scaled). Stars mark the mean per method; dashed lines indicate constant total cost.

Parameter Estimation

Parameter estimation studies how to infer unknown quantities in statistical, physical, and machine-learning models from observed data.

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Abstract

Parameter Estimation

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