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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