NeuralBES: A Differentiable, Control-Aware Emulator for Scalable Building Energy Modeling

Ting-Yu Dai; Takuya Kurihana; Wing Yee Au; Hon Yung Wong

cs.LGOct 7, 2026

NeuralBES: A Differentiable, Control-Aware Emulator for Scalable Building Energy Modeling

Authors: Ting-Yu Dai, Takuya Kurihana, Wing Yee Au, Hon Yung Wong

Organizations: Fujitsu Research of America

Abstract

Demand-side flexibility i.e. forecasting, shifting, and curtailing residential energy loads, depends on thermal models trusted across millions of heterogeneous buildings. Existing tools force a hard tradeoff: high-fidelity physics simulators such as EnergyPlus are accurate but sequential and require per-building calibration, while purely data-driven sequence models scale but abandon the physical structure that makes their predictions trustworthy. We introduce NeuralBES (Building Energy Simulation), a differentiable emulator that resolves this tradeoff by parameterizing a resistance--capacitance (RC) based thermal model with a shared neural encoder: static building metadata such as floor area, vintage, and HVAC type is mapped to physically bounded capacitances, conductances, and equipment coefficients, which become the coefficients of a scalar linear recurrence solved via a log-space parallel scan, and a predictor--corrector loop closes the thermostat--temperature nonlinearity while preserving full-horizon gradient flow. Trained on the ResStock dataset across three climate zones, NeuralBES handles heterogeneous building archetypes, vintages, and climate zones within a single trained encoder, while black-box baselines produce statistically plausible but physically inconsistent trajectories. On the annual full-year rollout, NeuralBES is the only data-conditioned model that is simultaneously physics-valid and accurate to within 4 MAPE points of the strongest raw-error baseline, while operating at roughly an order of magnitude fewer parameters than the transformer and recurrent baselines; among physics-valid baselines at parameter parity it more than halves the MAPE of the grey-box RC alternative.

Figures & tables

Property	PINN [ 7 ]	Dissipative [ 12 ]	PCNN [ 10 ]	NeuralBES (ours)
Physics enforcement	soft penalty	stability regularizer	arch. constraints	analytical ODE
Parameters per building	shared	shared	shared	shared
Cross-building eval	reported	reported	reported	reported
Full-horizon gradients	via penalty	via BPTT	via BPTT	via parallel scan
Nonlinear controller	$\times$	$\times$	$\times$	predictor–corrector
Exposes $C,UA$ at each $t$	$\times$	$\times$	partial	$\checkmark$

Table 1: Conceptual positioning of NeuralBES relative to the closest physics-aware ML families. Rows name properties along the physics-enforcement, parameter-sharing, and gradient-flow axes; they are not accuracy numbers.

Figure 1 : Architecture of NeuralBES. Static building features are encoded into a shared latent representation that conditions four parameter heads: the thermal head produces the RC capacitances $C^{\text{air}}$ , $C^{\text{mass}}$ and coefficients $h^{\text{am}}$ , $UA^{\text{env}}$ ; the HVAC head produces heating and cooling capacities and COPs; the infiltration/solar head produces wind-dependent infiltration and solar gain coefficients; and the internal gains head maps occupancy schedules to $\dot{Q}^{\text{int}}$ . Together with precomputed weather-driven forcings, setpoint schedules, and initial conditions, these parameters drive a predictor-corrector loop that solves the two-node RC thermal ODE via a parallel linear recurrence, iterated three times to resolve the nonlinear thermostat feedback. Electrical consumption is recovered by applying outdoor-temperature COP derating to the final HVAC thermal loads. Colors of equation variables throughout the paper correspond to the head that produces them.

Metric		DLinear	LSTM	PatchTST	Roformer	PI-Roformer	RC	NeuralBES
# Params (M)		1.3	36.6	3.0	20.5	11.0	0.96	1.0
MAPE (%)	$Q_{\mathrm{heat}}$	$161.3_{\pm 39.8}$	$\mathbf{38.5_{\pm 0.1}}$	$52.4_{\pm 9.2}$	$67.8_{\pm 6.8}$	$65.9_{\pm 5.4}$	$86.5_{\pm 30.5}$	$41.5_{\pm 4.3}$
MAPE (%)	$Q_{\mathrm{cool}}$	$121.3_{\pm 22.9}$	$\mathbf{37.6_{\pm 1.7}}$	$46.2_{\pm 8.5}$	$85.3_{\pm 3.0}$	$80.6_{\pm 3.5}$	$92.5_{\pm 32.4}$	$41.3_{\pm 0.4}$
RMSE ( ∘ C)	$T_{\mathrm{in}}$	$3.43_{\pm 0.83}$	$\mathbf{1.48_{\pm 0.01}}$	$1.68_{\pm 0.13}$	$3.26_{\pm 0.08}$	$2.92_{\pm 0.41}$	$4.05_{\pm 0.52}$	$2.79_{\pm 0.03}$
Mode excl. [%]		$26.1_{\pm 27.2}$	$36.9_{\pm 18.0}$	$45.5_{\pm 22.2}$	$24.4_{\pm 8.5}$	$31.0_{\pm 28.1}$	$\mathbf{100.0_{\pm 0.0}}$	$\mathbf{100.0_{\pm 0.0}}$
Bounds [%]		$73.8_{\pm 27.2}$	$63.1_{\pm 18.0}$	$54.3_{\pm 22.2}$	$75.6_{\pm 8.5}$	$68.8_{\pm 27.9}$	$98.6_{\pm 1.4}$	$\mathbf{99.7_{\pm 0.1}}$

Table 2: Annual full-year (35,040-step) rollout on the multi-region ResStock test set. Among data-conditioned models, NeuralBES is the only one with structural physics validity (100% mode exclusivity, 99.7% bounds adherence). LSTM has marginally lower raw error on the HVAC channels but operates at

36\times

the parameter count and produces those numbers from physically inadmissible trajectories (mode exclusivity

36.9

%, bounds adherence

63.1

%). Among physics-valid models (NeuralBES vs. RC) at parameter parity, NeuralBES more than halves RC’s MAPE. Weekly-rollout numbers and per-region breakdowns: Appendix E .

Figure 2 :

T_{\mathrm{in}}

sensitivity to a uniform

T_{\mathrm{out}}

perturbation of

\{-5,-2,0,+2,+5\}\,^{\circ}

C. NeuralBES and RC give the physically expected monotone slope; Roformer and PI-Roformer over-react (indoor temperature shifts by more than

2\,^{\circ}

C for a

5\,^{\circ}

C outdoor perturbation, implying an implausibly leaky envelope); DLinear’s slope is shallow but in the right direction; PatchTST returns a flat zero response at every perturbation, i.e. its

T_{\mathrm{in}}

prediction is formally independent of

T_{\mathrm{out}}

Figure 3 : Multi-channel weekly rollouts on a representative multi-region test building. NeuralBES (blue) produces sparse, on/off load trajectories aligned with thermostat events. Baselines emit visibly noisy or near-constant predictions that violate the actual loads’ seasonal sparsity: DLinear (red) holds a persistent winter $Q_{\mathrm{cool}}$ ; Roformer (green) shows high-frequency winter $Q_{\mathrm{heat}}$ oscillations orders of magnitude below the real events (note the $10^{-7}$ vs. $10^{-4}$ axis scales); PatchTST emits non-zero summer $Q_{\mathrm{heat}}$ . On $T_{\mathrm{in}}$ , NeuralBES tracks envelope-driven excursions while LSTM and PatchTST flatten near the setpoint mean.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4 : Per-day MAE on the three-state (multi-region) weekly rollouts, aggregated across 672-step windows and stratified by target channel.

Q_{\mathrm{heat}}

(left) errors concentrate in winter (low

T_{\mathrm{out}}

);

Q_{\mathrm{cool}}

(middle) errors bulge in summer (days 150–240);

T_{\mathrm{in}}

(right) errors follow the seasonal envelope in which the envelope–infiltration dynamics are most stressed. NeuralBES stays in the bottom tier of curves for both HVAC channels: flat and low on

Q_{\mathrm{heat}}

, and matching PatchTST and LSTM near the summer

Q_{\mathrm{cool}}

peak. DLinear’s

Q_{\mathrm{heat}}

error is elevated across seasons and RC’s

Q_{\mathrm{cool}}

peaks sharply during the summer maximum, consistent with the seasonal rollout trajectories in Figure 3 (main text).

Figure 5 : Ramp-rate distribution of

\Delta T_{\mathrm{in}}

per 15 min (log density) on the multi-region weekly rollouts. NeuralBES matches the central spike and the heavy tails of ResStock ground truth; RC and DLinear produce over-wide distributions that over-predict large ramps; LSTM, Roformer, and PI-Roformer recover the central spike with slightly broader tails.

Figure 6 : MAE improvement of NeuralBES over each baseline (in percent of baseline MAE), stratified by outdoor temperature

T_{\mathrm{out}}

, on the multi-region test set. Negative values indicate NeuralBES is better; the magnitude is the relative error reduction. Note the different vertical scales:

Q_{\mathrm{heat}}

is in units of

10^{6}

% because DLinear’s error blows up when

T_{\mathrm{out}}>25\,^{\circ}

Q_{\mathrm{cool}}

peaks around

-1500

% for DLinear near

T_{\mathrm{out}}=10\,^{\circ}

C, and

T_{\mathrm{in}}

degradation is largest for DLinear and RC in cold regimes (

T_{\mathrm{out}}<0\,^{\circ}

C).

Region	Metric		DLinear	LSTM	PatchTST	Roformer	PI-Roformer	RC	NeuralBES
CA	MAPE (%)	$Q_{\mathrm{heat}}$	192.65	88.50	130.74	67.80	63.91	91.20	66.75
	MAPE (%)	$Q_{\mathrm{cool}}$	258.79	58.43	94.41	49.25	45.62	72.44	50.45
	RMSE ( ∘ C)	$T_{\mathrm{in}}$	2.94	2.01	2.09	1.70	1.62	2.66	2.63
NY	MAPE (%)	$Q_{\mathrm{heat}}$	76.46	34.38	34.01	30.67	35.19	97.82	30.68
	MAPE (%)	$Q_{\mathrm{cool}}$	119.41	46.45	50.00	40.20	41.18	107.96	42.54
	RMSE ( ∘ C)	$T_{\mathrm{in}}$	2.62	1.76	1.43	1.36	1.61	2.81	1.98

Appendix

Table 3: Weekly-rollout (672-step) comparison on the ResStock test buildings. The top block reports per-target errors stratified by region:

Q_{\mathrm{heat}}

and

Q_{\mathrm{cool}}

as MAPE (%),

T_{\mathrm{in}}

as RMSE ( ∘ C). The bottom block reports mode exclusivity and bounds adherence (defined in Section 4.2 ) on the Multi rollout.

Figure 7 : Specific failure-mode case study: two-week

T_{\mathrm{in}}

rollouts for a single multi-region test building across four seasons. In the fall panel, the ground truth (black dashed) swings between

\sim 22

and

\sim 26\,^{\circ}

C following a setpoint excursion, while Roformer (green) and PI-Roformer (yellow) sit flat at

\sim 21\,^{\circ}

C and fail to track the thermal interaction at all. In summer, Roformer drops to

\sim 16\,^{\circ}

C and stays flat while the ground truth oscillates between

\sim 16

and

\sim 18\,^{\circ}

C; only NeuralBES (blue) reproduces the diurnal swing. Winter and spring panels show all models behave reasonably: the failure is regime-specific to seasons in which envelope-driven dynamics dominate.

Model	Family	Static injection	Key architectural choice
DLinear [ 38 ]	linear	additive bias	trend/seasonal decomposition
LSTM	recurrent	FiLM (id-init)	hidden 512, 6 layers
PatchTST [ 22 ]	transformer	FiLM (id-init)	patching 48/24, RevIN, channel-indep.
Roformer [ 31 ]	transformer	FiLM (id-init)	encoder–decoder, RoPE
PI-Roformer	hybrid	FiLM (id-init)	Roformer + 2R2C head w/ flux correction
RC Grey-Box	physics	encoder-predicted params	2R2C w/ fixed COPs, fixed setpoint band

Appendix

Table 4: Baselines compared in this paper. PI-Roformer tests whether a shallow trunk-plus-physics-head hybrid suffices or whether the full NeuralBES integration is needed.

Model	Hidden $d$	Layers	Heads	Dropout	Batch	LR
DLinear	512	1	—	0.0	512	$1.0\!\times\!10^{-4}$
LSTM	512	6	—	0.2	256	$1.0\!\times\!10^{-4}$
PatchTST	128	3	4	0.1	128	$1.0\!\times\!10^{-4}$
Roformer	512	6	8	0.2	128	$1.0\!\times\!10^{-4}$
PI-Roformer	512	3	8	0.0	256	$1.0\!\times\!10^{-4}$
RC Grey-Box	128	1	—	0.0	512	$1.0\!\times\!10^{-4}$

Appendix

Table 5: Baseline hyperparameters for the multi-region runs. PatchTST uses patch length 48 (12 h) and stride 24 (6 h) on the 15-minute series. NeuralBES has no transformer/recurrent depth in the conventional sense:

d{=}512

is the shared embedding dimension produced by the static encoder and consumed by the parameter heads of Appendix C . All runs use AdamW with weight decay

10^{-2}

, gradient clipping at norm 1.0, and a 2000-step linear LR warmup.

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Open paper AskPDF arXiv

The building energy community lacks a foundational thermal model, i.e., a single pretrained model capable of generalizing across diverse buildings, climates, and control strategies without building-specific calibration. Achieving this vision requires architectural principles that capture universal thermal dynamics rather than memorizing building-specific patterns. We take a step toward this goal by presenting a physics-informed transformer architecture that embeds domain knowledge, e.g., derivative enrichment and Euler-based numerical integration, into a decoder-only framework. We incorporate static building features extracted from simulation models and employ Rotary Position Embedding attention to capture temporal dependencies. Evaluated on the CityLearn dataset spanning 247 residential buildings across three climate zones, our model achieves one-step prediction accuracy (RMSE of 0.30°C in Texas, 0.29°C in Vermont) while outperforming both traditional baselines and fine-tuned Time-Series Foundation Models. We also demonstrate zero-shot transferability: models trained on as few as two buildings generalize to unseen buildings and climate zones without fine-tuning. Despite the limitation of simulated residential buildings, our results establish physics-informed architectural principles as a promising foundation for universal building thermal models.

Abstract

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