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

The gist: NeuralBES introduces a differentiable emulator that resolves the tradeoff between high-fidelity physics simulators and scalable data-driven models by parameterizing an RC thermal model with a shared neural encoder and solving the resulting linear recurrence in parallel via a log-space scan, while closing the thermostat–temperature nonlinearity through a predictor–corrector loop.

Problem Addressed

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. Classical BEM requires per-building calibration of dozens of parameters (wall layers, window properties, HVAC performance curves, infiltration coefficients), which is what gives it accuracy and what prevents it from scaling. Purely data-driven emulators scale but abandon the physical structure that makes their outputs trustworthy under distribution shift (new climates, new control policies, new tariffs), which is precisely the regime where demand-flexibility studies need them most. NeuralBES targets the middle.

NeuralBES Architecture and Parameterization

NeuralBES parameterizes 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. The architecture involves a neural encoder that reads the static descriptor and produces both a latent building embedding zb and a set of building-specific thermal parameters that populate an RC model. Each head (color-coded in Figure 1) is a two-layer SiLU MLP conditioned on the static embedding zb, with a zero-initialized final layer and a bounded activation so that capacitances, conductances, capacities, and COPs remain strictly positive and in physically plausible ranges.

Solving the Thermal Dynamics

The time-varying signal wb,t then acts as the external forcing on this model. The air-node balance in Eq. (1) reduces to a scalar linear ODE of the form dTair b dt = −P air b,t Cair b Tair b − Tair,eq b,t, Pair b,t = UAinfil b(t) + h am b,(3). This ODE admits an exact closed-form solution over [t, t + ∆t], a geometric decay toward the instantaneous equilibrium. Introducing the affine term bair b,t = (1 − αair b,t) Tair,eq b,t puts the update in the familiar state-space form Tair b,t = αair b,t TAir b,t−1 + bai airb,t.

Parallel Computation and Control Loop

The recurrence is solved in parallel across time using a log-space associative scan. The Heinsen log-space reformulation avoids underflow by working with cumulative log-decays. This process is performed in adaptively-sized chunks to prevent overflow and maintains efficiency at long horizons. The coupling between state and actuator is closed through a short fixed-point loop that alternates between estimating the load the thermostat would demand at the current trajectory, clipping that demand by equipment capacity, and re-integrating the temperature trajectory under the clipped load. This predictor–corrector loop closes the thermostat–temperature nonlinearity.

Performance and Comparison

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. Among physics-valid baselines at parameter parity it more than halves the MAPE of the grey-box RC alternative. NeuralBES achieves 100% mode exclusivity and 99.7 ± 0.1% bounds adherence on the multi-region ResStock test set. The model is roughly an order of magnitude smaller than transformer and recurrent baselines because of its physical inductive bias, not because of architectural tricks.

Limitations

Two limitations frame the next steps. First, NeuralBES resolves only the sensible thermal dynamics of the zone air and building mass and does not explicitly model the domestic hot-water system, which is absent from the heat-balance equation that drives the analytical solver. Second, scalability along the physics axis is bounded by the equations we commit to: adding phenomena such as multi-zone coupling, refrigerant cycles, or stratified storage requires editing the governing ODE rather than widening the network. The more interesting research target going forward is how to extend the data-driven component so that it can absorb phenomena hard to express analytically while keeping the interpretability and generalization properties that the physical backbone provides.

Conclusion

We introduce NeuralBES, a differentiable building-energy emulator that parameterizes a two-node RC thermal model with a shared encoder and solves the resulting linear recurrence in parallel via a logspace associative scan, wrapped in a predictor–corrector loop that closes the thermostat–temperature nonlinearity. On the multi-region ResStock annual-rollout benchmark, NeuralBES is the only dataconditioned model on the Pareto frontier of accuracy and physics validity (100% mode exclusivity, 99.7% bounds adherence across seeds), at roughly an order of magnitude fewer parameters than transformer and recurrent baselines, while substantially outperforming the comparably structured grey-box RC at parameter parity (∼ 41% vs. ∼ 89% MAPE on the HVAC channels). First-principles thermodynamics and scalable neural sequence modeling share the same forward pass. The code, including the script to gather the public dataset, is attached in the supplement materials to reproduce the result. All cited assets are publicly released under their respective open licenses and are used consistently with their terms. The work uses only synthetic, simulator-generated building energy traces from the publicly released ResStock corpus (Section 4.1) and involves no human subjects, personally identifiable information, or scraped content. The work uses only synthetic, simulator-generated building energy traces from the publicly released ResStock corpus (Section 4.1) and involves no human subjects, personally identifiable information, or scraped content. The code, including the script to gather the public dataset, is attached in the supplement materials to reproduce the result. All cited assets are publicly released under their respective open licenses and are used consistently with their terms. The work uses only synthetic, simulator-generated building energy traces from the publicly released ResStock corpus (Section 4.1) and involves no human subjects, personally identifiable information, or scraped content. All cited assets are publicly released under their respective open licenses and are used consistently with their terms. The work uses only synthetic, simulator-generated building energy traces from the publicly released ResStock corpus (Section 4.1) and involves no human subjects, personally identifiable information, or scraped content. All cited assets are publicly released under their respective open licenses and are used consistently with their terms. The work uses only synthetic, simulator-generated building energy traces from the publicly released ResStock corpus (Section 4.1) and involves no human subjects, personally identifiable information, or scraped content. All cited assets are publicly released under their respective open licenses and are used consistently with their terms. The work uses only synthetic, simulator-generated building energy traces from the publicly released ResStock corpus (Section 4.

1. Better demand-side flexibility via NeuralBES: The system can forecast, shift, and curtail residential energy loads with accuracy 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.

2. Physics-valid generalization: The improved system can handle heterogeneity by mapping static building metadata such as floor area, vintage, and HVAC type is mapped to physically bounded capacitances, conductances, and equipment coefficients, allowing it to function across heterogeneous building archetypes, vintages, and climate zones within a single trained encoder.

3. Scalable inference: The system can simulate populations of buildings efficiently because the core mechanism is a log-space parallel scan which runs in O(T) work and O(log T) depth via a parallel scan, translating directly into parameter efficiency at long horizons compared to attention-based models that incur O(T 2) compute and memory.

4. Physics-constrained control: The system can manage real-world operational constraints by using a predictor–corrector loop that closes the thermostat–temperature nonlinearity, ensuring it maintains exclusive heating/cooling modes, bounded indoor temperature, [and] correct sign of HVAC response where purely data-driven baselines collapse to statistically plausible but physically inconsistent trajectories.

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.