Energy-efficient operation of neural operators for virtual sensing

Jason Yoo; Samrendra Roy; Souvik Chakraborty; Syed Bahauddin Alam

cs.LGSep 24, 2026

Energy-efficient operation of neural operators for virtual sensing

Authors: Jason Yoo, Samrendra Roy, Souvik Chakraborty, Syed Bahauddin Alam

Organizations: Nuclear, Plasma & Radiological Engineering Department, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, USA · Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, India · Yardi School of Artificial Intelligence, Indian Institute of Technology Delhi, New Delhi, India · National Center for Supercomputing Applications, Urbana, IL, USA

Abstract

Virtual sensing repeatedly reconstructs physical fields from changing observations, often on a fixed geometry. We investigate how shared spatial computation reduces the energy of these updates while retaining the selected checkpoint and its evaluated predictions. In a heat-exchanger service, standard compiler freezing and explicit trunk reuse give similar operating energy reductions relative to graph replay: approximately 1% at one request per second and 20% at forty requests per second. In 15 W mode with fixed clocks, reuse with graph replay completes the same request sequence with 22.0 to 22.5% less energy than eager execution, including preparation and waiting. DeepONet and Fourier neural operator (FNO) controls distinguish the effects of reusable arithmetic and launch overhead. Preparation, artifact construction, and worker replacement add costs outside repeated inference. These results connect operator structure to operating energy and show how update frequency and execution lifetime govern the benefit of computation reuse in physical-field virtual sensing.

Figures & tables

Figure 1: Trunk reuse reduces heat-exchanger inference energy. a , The spatial representation is retained; branches and contraction process each new input. b , Predicted pressure and velocity at all 3,977 released $y$ – $z$ query coordinates for CFD test case 1244, shown without spatial interpolation. c,d , Module energy per request and block-median response latency for eager (E), graph (G), trunk reuse (R) and reuse with graph (RG). Points are fresh-process blocks ( $n=4$ per path); horizontal marks give medians. Reductions are medians of paired ratios to E. Each path includes raw CPU input and decoded CPU output. Energy covers 20 s of continuous inference at the retained MAXN configuration (Supplementary Note Supplementary Note 1. Heat-exchanger execution costs and source comparison ), without idle subtraction. All 310 saved fields agree with the device-local reference before and after decoding.

Figure 2: Energy savings persist over complete service operation. a–d , Completion fraction, response-time p95, mean module power during arrivals, and energy from preparation through closure. E and RG use the same transport and numerical checks. Points are fresh-worker blocks; lines pair repeats (

n=3

per condition). Both paths complete all 7,200 arrivals at 15 W fixed clocks and 60 Hz. Shaded conditions have unequal completed work. Mode labels denote configured power policies. Total energy includes the 20 s warmup and waiting, without idle subtraction; input-bank loading and cooling are excluded.

Figure 3: The energy benefit depends on operator structure. DeepONet ( a ) and FNO ( b ) services on Jetson, A2000 and RTX 5060 Ti, from left to right. Points show block-median response latency and interval energy per completed request (

n=3

per arm and device); grey lines join paired blocks. Printed values are median paired ratios:

G_{T}/G_{0}

for trunk reuse and

G_{0}/E

for graph replay. Offered rates and energy domains differ between devices, so comparisons are within each device. All returned outputs match the local reference. Header counts include

G_{H}

, omitted from the plot; complete costs and graph-baseline contrasts are in Supplementary Tables 8 and 9 .

Figure 4: Standard freezing obtains the reuse benefit, subject to operating costs. a , Preparation-to-closure energy for six heat-exchanger paths at 40 Hz over 30 s. Open and filled points distinguish two sessions, each with three fresh-worker blocks per path; bars mark medians. F denotes standard freezing; other paths follow Fig. 1 . b , Paired energy reductions relative to native graph over 120 s at each request rate. c , Freezing with graph at 10 Hz, with the artifact prebuilt or construction charged to each episode. Points in b,c are medians of three episode pairs. The construction charge uses the median of five fresh-process builds; whiskers span the observed episode pairs and, where charged, all five build costs. Lines guide the eye; negative reductions denote increased energy. All service blocks use 15 W automatic clocks, complete equal work and include preparation, waiting and closure without idle subtraction.

Extended Data Fig. 1: Energy saving includes preparation and warmup. a , Module power for three paired E and RG blocks at 15 W fixed clocks and 60 Hz. Curves are one-second time-weighted means, split at phase boundaries; time zero is the first arrival. b , Energy by phase, integrated from the original samples, on a logarithmic axis. Points are blocks; lines pair repeats. c , Cumulative paired reduction through each phase. All blocks complete 7,200 requests, with a final reduction of 22.0–22.5%. Preparation includes qualification; the 20 s warmup is retained. Energy is not idle-subtracted; bank loading and cooling are excluded.

Extended Data Fig. 2: Fixed-trunk reuse removes repeated DeepONet work. a , Retaining four trunk layers over six query chunks removes 58.6 GFLOP per request for 86.5 MiB of storage. Dense calls fall from 28 to four; six contractions remain unchanged. b , Decoded relative

L_{2}

errors against truth for 16 input-bank cases per model. Reference and candidate markers coincide;

e_{j}

denotes the error for input-bank case

j

. Models use different native grids; the complete audit contains 80 comparisons (Supplementary Table 11 ). c , Response latency for the RTX 5060 Ti DeepONet blocks in Fig. 3 a. Points are block medians (

n=3

per arm); bars mark arm medians.

Extended Data Fig. 3: Rebuilding a worker preserves the target but interrupts service. a , Twelve traces (

n=3

per arm and fault). Power-mode changes at 10 and 20 s retain the worker. A weight mutation or exit at 30 s triggers replacement; red intervals end when the new worker qualifies against the original target. Events occur between requests. b,c , Replacement time and module energy, including controller instrumentation. Each point is one trace. Replacement energy is part of the trace total. All returned outputs match the target; unavailable arrivals and queue refusals are counted separately in Supplementary Note Supplementary Note 2. Heat-exchanger service energy and execution controls .

Field	Source error (%)	Jetson error (%)	Max. difference	Max. error increase
$p$	0.8188057	0.8188016	0.017578	9.16e-06
$u_{z}$	1.4538439	1.4538449	7.6294e-06	7.7e-06
$u_{y}$	1.0175234	1.0175252	1.1273e-05	3.98e-06
$u_{x}$	0.5205477	0.5205475	2.6464e-05	1.44e-06

Table 1: Physical-output comparison on all 310 original test cases. Relative

L_{2}

entries are means in percent. Maximum field differences use Pa for pressure and m s -1 for velocity. The final column is the largest per-case increase in relative error, in percentage points. All Jetson arms share these arrays.

Arm	Latency (ms)	Energy (J/request)	Allocated (MiB)	Reserved (MiB)
E	6.527 [6.492, 6.567]	0.1087 [0.1062, 0.1089]	70.35	82
G	4.439 [4.433, 4.452]	0.0886 [0.0872, 0.0888]	70.82	112
R	3.360 [3.294, 3.370]	0.0430 [0.0427, 0.0434]	70.35	82
RG	1.453 [1.448, 1.467]	0.0258 [0.0254, 0.0259]	118.82	140

Table 2: Continuous-inference costs at the recorded Jetson configuration. Medians and observed ranges over four process blocks per path; latency is the median over requests within each block. E, eager; G, graph; R, trunk reuse; RG, reuse with graph. Memory is peak CUDA allocator usage, not total module RAM. All paths preserve the evaluated local outputs.

Policy	Arm	Rate (Hz)	Returned	p95 (ms)	Power (W)	Energy (J)
15 W auto	E	10	1200	21.97	5.549	841.9
15 W auto	RG	10	1200	8.07	5.202	799.4
15 W auto	E	60	5760	119.98	7.452	1071.2
15 W auto	RG	60	7200	7.15	5.952	889.6
15 W fixed	E	10	1200	11.76	5.960	944.7
15 W fixed	RG	10	1200	4.55	5.582	885.7

Table 3: Heat-exchanger service across operating conditions. Medians of three fresh-worker blocks per condition. Power covers arrivals; total energy covers preparation, warmup, arrivals, drain and closure, excluding bank loading and cooling. At 60 Hz with automatic clocks, E and RG complete unequal work.

Session	Path	p95 (ms)	Preparation (J)	Total (J)
1	E	21.28	21.26	228.78
1	G	16.86	22.00	225.55
1	R	11.46	20.24	185.35
1	RG	7.28	20.81	183.38
1	F	10.00	20.78	184.99
1	FG	6.83	21.61	183.74

Table 4: Matched heat-exchanger service with standard freezing. Each session has three fresh workers per path at 40 Hz over 30 s; every block returns all 1,200 requests with matching outputs. Entries are medians. E, G, R and RG denote eager, graph, manual reuse and their combination; F and FG denote freezing without and with graph. Total energy includes preparation through closure.

Path	Rate (Hz)	Time (s)	Requests	p95 (ms)	Prep. (J)	Total (J)
G	1	120	120	18.91	21.92	585.93
RG	1	120	120	9.75	20.75	579.92
FG	1	120	120	9.17	21.43	581.15
G	10	10	100	17.70	21.82	77.95
RG	10	10	100	7.88	20.65	73.06
FG	10	10	100	7.50	21.38	73.68

Table 5: Dependence on request rate and episode duration. Three fresh-worker blocks per row at 15 W with automatic clocks and no additional warmup. Each block completes all offered requests with matching outputs. Costs and response-time p95 are block medians. Frozen-artifact construction is excluded and reported separately.

Model	Path	Rate (Hz)	Requests	p95 (ms)	Total (J)
DeepONet	E	1	120	154.24	704.81
DeepONet	G	1	120	154.01	709.23
DeepONet	R	1	120	31.44	588.79
DeepONet	RG	1	120	33.01	588.82
FNO	E	1	120	25.98	620.11
FNO	G	1	120	24.71	620.72

Table 6: Darcy and FNO service costs. All requests return matching outputs in each of three blocks per row at 15 W with automatic clocks. Entries are medians; preparation-to-closure energy includes waiting. Absolute costs do not rank models with different grids. The incomplete Darcy 8 Hz condition is described in the text.

Primary comparison: fresh-worker blocks
Service	Returned/7,200	Response age (ms)	Round trip (ms)	Module power (W)	Recovery (s)
OpCert (pair 0)	7200	6.79	6.71	5.94	4.42
Ray Serve (pair 0)	5391	113.59	21.61	6.39	11.67
OpCert (pair 2)	7200	6.86	6.78	5.94	4.44
Ray Serve (pair 2)	5388	113.48	21.61	6.38	11.76
Ray Serve (pair 3)	5386	113.47	21.61	6.38	12.01

Table 7: Matched application logic under two serving frameworks. Response age and round trip are block medians of arrival-to-response and dispatch-to-response times. Mean module power includes controller activity, output auditing and waiting. Recovery is explicit in OpCert and automatic in Ray with one-second health checks. Primary pairs use OpCert–Ray, OpCert–Ray and Ray–OpCert order; excluded and unmatched blocks remain shown.

DeepONet
Device / arm	Rate	Response	Energy	Prep.	Alloc.	Reserv.
	(Hz)	(ms)	(J/request)	(s)	(MiB)	(MiB)
5060 Ti E	48	11.615	1.817	1.458	101.5	222.0
5060 Ti $G_{0}$	48	11.545	1.811	1.488	166.2	308.0
5060 Ti $E_{T}$	48	4.613	0.482	1.353	188.1	254.0
5060 Ti $G_{T}$	48	4.484	0.480	1.336	252.7	286.0

Table 8: All execution paths in the paced-service cohort. Entries are medians over three blocks. E, qualified eager;

G_{0}

, prepared DeepONet or native FNO graph;

E_{T}

, explicit trunk eager;

G_{T}

, explicit trunk graph;

G_{H}

, empirical-pass graph. Memory is the qualification snapshot, not a peak. Energy is GPU-total on desktops and module-input on Jetson. Preparation ends at readiness and is outside request energy.

DeepONet
Device	Contrast	Response reduction (%)	Energy reduction (%)
5060 Ti	$E\to G_{0}$	0.46 [0.06, 1.64]	0.19 [-0.17, 0.33]
5060 Ti	$E\to E_{T}$	60.28 [59.31, 60.79]	73.42 [73.36, 73.87]
5060 Ti	$G_{0}\to G_{T}$	61.16 [61.16, 66.78]	73.49 [73.25, 73.69]
5060 Ti	$E_{T}\to G_{T}$	4.99 [2.58, 16.41]	-0.52 [-0.58, 0.59]
5060 Ti	$G_{0}\to G_{H}$	-0.18 [-1.10, 0.28]	-0.15 [-0.67, -0.13]

Table 9: Matched contrasts separate execution mechanisms. Each cell gives median percentage reduction and observed range over three paired groups. Negative values indicate increases. Each contrast uses the same request trace and service boundary.

Quantity	Eager	Graph	Reuse
Parent measured interval (ms)	186.276	184.113	57.781
GPU kernel-duration sum (ms)	137.698	Not resolved	Not resolved
GPU graph-interval sum (ms)	n/a	138.294	6.806
CUDA graph launches	0	16	16
Host-to-device bytes	34030336	34030272	34030272
Device-to-host bytes	11343424	11343424	11343424

Table 10: Instrumented service trace over 16 measured requests on RTX 5060 Ti. The parent interval contains client/service activity. GPU entries are sums of individually traced kernel durations for eager, or graph execution intervals for graph and reuse. The latter do not expose individual kernels inside replay. These overlapping timing categories are not additive.

Model and native grid	Candidate	Normalised exact	Decoded exact	Mean relative $L_{2}$
DeepONet, $421\times 421$	Checked eager	16/16	16/16	0.0848994
	Graph	16/16	16/16	0.0848994
	Reuse	16/16	16/16	0.0848994
FNO, $85\times 85$	Checked eager	16/16	16/16	0.0172171
	Graph	16/16	16/16	0.0172171

Table 11: Darcy outputs before and after physical decoding. Three DeepONet paths and two FNO paths each use positions 8–23 on RTX 5060 Ti, giving 80 comparisons. Counts denote complete-output agreement with each reference; relative

L_{2}

is the mean error against truth on the native grid. Graph denotes

G_{H}

in this separate audit.

Checkpoint / task	Original	Deterministic	Original	Deterministic
	Jetson		RTX 5060 Ti
DeepONet, Burgers $r512$	P	P	–	–
DeepONet, Darcy $r421$	P	P	–	–
FNO, Burgers $r512$	P	P	–	–
FNO, Darcy $r85$	P	P	–	–
NEUTRON, lid-driven cavity	N	P	P	P

Table 12: Complete reference, hoisting and graph outcomes for the 42 configuration cells. Original and deterministic configurations of a checkpoint are separate cells, not independent applications. P: eager repeated and both hoisting and graph capture agreed. F: eager repeated and hoisting agreed, but graph construction failed. U: eager repeated and hoisting agreed, but graph was unavailable. N: eager did not repeat, so candidates were not qualified. A dash denotes an untested checkpoint/configuration.

	Latency (ms)			Energy (J/request)
Device	Eager	Graph	Reuse	Graph	Reuse
H200	2.642	2.188	0.430	1.1375	0.0850
GH200	4.911	2.392	0.566	1.1362	0.1101
A100	6.941	6.169	0.727	1.9550	0.1115
A40	8.882	8.232	0.857	2.4042	0.1192
RTX 5060 Ti	10.894	10.700	0.693	1.8769	0.0606

Table 13: Prepared-input Darcy DeepONet costs on seven devices. Medians of three fresh-process blocks. Latency spans device input to owned device output. Energy uses separate saturated intervals without setup or warmup; eager energy was not recorded. Discrete devices report GPU energy and Jetson reports module-input energy. Compare paths within each device.

Grid	Graph (ms)	Reuse + graph (ms)	Paired speedup
$85^{2}$	0.5661	0.2587	2.209 (2.164–2.266)
$141^{2}$	1.2585	0.2753	4.565 (4.550–4.647)
$211^{2}$	2.7645	0.3245	8.518 (8.421–8.656)
$281^{2}$	4.8058	0.4656	10.327 (10.322–10.725)
$421^{2}$	10.7004	0.6929	15.435 (15.431–15.561)

Table 14: Reuse relative to a graph-based execution with the same supervisor. Latencies are arm medians; speedup is the median of three paired process ratios with observed range. This is a prepared-device-input cohort, not the full service.

	High cap	Low, retained	Low, reclaim	Restore / recover
Ordinary eager	18 exact	18 exact	3 refusals	9 exact
Dedicated-pool eager	18 exact	18 exact	18 exact	9 exact
Prepared graph	18 exact	18 exact	18 exact	9 exact

Table 15: Storage-policy control on RTX 5060 Ti. Counts sum three worker episodes per policy with the same ordered input sequence. Refusal ends that phase. Dedicated-pool episodes are a subsequent control, not paired performance blocks.

Figure 1: Allocator-cap sensitivity and physical prediction error. a , Rayleigh–Bénard on RTX 5060 Ti, one fresh process per cap: fraction of changed elements and relative $L_{2}$ to the unrestricted output. Crosses mark no output at 0.15 GiB. The pressure scale is $P=A_{\mathrm{peak}}+W_{\max}$ . b , Test window 120: unrestricted and capped predictions, their absolute difference, and unrestricted prediction error against the next state. Both predictions have one-step VRMSE 0.0242. Numerical-setting and external-occupancy controls are in Supplementary Table 16 .

Figure 2: Storage retention and plan-cache policy separate continuation from recovery. a,b , Relative

L_{2}

to the first output over six calls on RTX 5060 Ti and GH200. Caps change from 0.70 to 0.30 to 0.70 GiB. Three processes per policy coincide. After restoration, pool-release outputs remain different with the cache enabled but recover the initial output with the cache disabled. c,d , Reserved and allocated memory per call. Labels give low-cap allocator refusals (RTX: 12 and 10; GH200: 38 and 36). There are nine fresh processes per device.

Control	Relative $L_{2}$	Differing elements (of 262,144)	Allocator refusals	Note
Default settings	$7.75\times 10^{-4}$	261,675	16	0.20 GiB cap versus unrestricted; TF32 on, benchmark off
cuDNN deterministic	$7.75\times 10^{-4}$	261,675	16	0.20 GiB cap versus unrestricted; same output digest as default
Deterministic algorithms and CUBLAS workspace configuration	$7.75\times 10^{-4}$	261,675	16	0.20 GiB cap versus unrestricted; same output digest as default
TF32 off on both sides	$2.87\times 10^{-6}$	257,327	5	0.20 GiB versus 0.35 GiB cap; magnitude reduced, bits still differ
External process holds 14.8 GiB; no allocator cap	0	0	0	Uncapped; byte-identical to the unrestricted output

Table 16: Numerical-setting and external-occupancy controls. Seeded Rayleigh–Bénard, fixed checkpoint and GPU. Rows 1–3 compare a 0.20 GiB cap with unrestricted execution; row 4 uses a 0.35 GiB reference. The final row applies external occupancy without an allocator cap. Counts describe this single-input diagnostic.

Device and candidate	$E_{\rm bit}$	$E_{\rm num}$	$E_{\rm field}$
5060 Ti, DeepONet	0/8; 0/16	8/8; 16/16	8/8; 16/16
5060 Ti, FNO	0/8; 0/16	0/8; 0/16	8/8; 16/16
A2000, DeepONet	0/8; 0/16	8/8; 16/16	8/8; 16/16
A2000, FNO	0/8; 0/16	0/8; 0/16	7/8; 15/16
Jetson, TensorRT	0/8; 0/16	8/8; 16/16	8/8; 16/16

Table 17: Qualification and evaluation outcomes for runtime transitions. Each entry gives passing witnesses out of eight, followed by passing evaluation inputs out of 16. Candidates are compiled PyTorch except the specialised Jetson TensorRT engine. Counts are offline output comparisons; live gates are reported in Supplementary Fig. 3 c.

Figure 3: Illustrative field and flux budgets change admission decisions. a , Darcy FNO on RTX 5060 Ti, evaluation position 8: coefficient, decoded reference, compiled–reference field difference and gradient-difference magnitude. The line marks the flux section at $y=0.5$ . b , FNO execution changes relative to reference errors on RTX 5060 Ti for eight qualification and 16 evaluation inputs. Colours and markers distinguish field, gradient and flux; the dashed line is $\eta=0.01$ . c , Live startup decisions; grey cells denote offline evaluation. Offline counts for the bitwise, numerical and field criteria, including A2000 FNO failures, are in Table 17 . These budgets are not application acceptance thresholds.

Model	Candidate	Gate	Response (ms)	Energy (J/request)
DeepONet	Fixed-trunk graph	$E_{\rm bit}$	1.43 (1.42–1.45)	0.339 (0.335–0.343)
DeepONet	Compile	$E_{\rm num}$	9.18 (9.13–9.22)	1.604 (1.593–1.613)
FNO	Native graph	$E_{\rm bit}$	0.780 (0.774–0.790)	0.0882 (0.0876–0.0886)
FNO	Compile	$E_{\rm field}$	1.28 (1.25–1.29)	0.0930 (0.0928–0.0934)

Table 18: Contemporaneous service measurements of qualified candidates. Six fresh-worker blocks per arm on RTX 5060 Ti, alternating AB/BA order within each model’s session. Entries are arm medians with observed min–max ranges. The relation column gives the gate used in the measured blocks; separate admission tests are reported in Supplementary Fig. 3 c.

Configuration	Detection	Incorrect replies	Recovery outcome
Guard with recovery	Before publication	0	Ready after requalification
Recovery withheld	Before publication	0	QUARANTINED
Periodic check	After window closes	16	Not attempted

Table 19: Service state after weight mutation with recovery invoked or withheld. RTX 5060 Ti, one weight-mutation run per model and configuration. Both models gave the same qualitative outcome; the retained-target row uses the archived guarded pilot.

Predictor	Locations	$I$ rel. $L_{2}$ (%)	$T$ rel. $L_{2}$ (%)	$I$ RMSE (A/segment)	$T$ RMSE ( ∘ C)
MIMONet	All 324	1.3298	0.05294	0.001454	0.03744
Ridge	All 324	0.09917	0.01564	0.0001090	0.01063
MIMONet	Withheld 292	1.3212	0.05311	0.001445	0.03756
Ridge	Withheld 292	0.1028	0.01647	0.0001131	0.01120

Table 20: Chronological fuel-cell reconstruction accuracy. All entries use the same 2,642 test frames and physical targets. Relative

L_{2}

is averaged over frames; RMSE pools frames and the indicated locations. Both predictors use the same 32 selected grid locations and training-only normalisation. Temperature targets inherit the released spatial interpolation from 81 measured locations.

Quantity	OpCert	Ray Serve
Predictions returned / 121	117	114
Observations without a current prediction	4	7
Maximum field age (s)	5	8
Fault-to-first-reply interval (s)	4.006–4.008	7.005–7.010
Module energy over 120.998 s (J)	612.308–613.437	632.421–633.427
Segment-current RMSE from fresh prediction	0.06112	0.08006

Table 21: Delivery and field error on the recorded fuel-cell segment. Three repeats per service yield the same delivered sequence. Errors pool 121 observation intervals and 292 withheld grid locations. Segment-current magnitudes are in mA/segment and temperature in ∘ C. Time and energy entries are observed ranges over three replays. Energy includes replacement and waiting but excludes initial preparation and shutdown. The consumer holds the latest field between replies.

Figure 4: Holding an earlier prediction changes field error. a,b , Segment-current magnitude and interpolated temperature fields; markers locate 32 sampled grid locations. c , Mean temperature at 292 withheld grid locations; shading marks the device-replay interval. d,e , RMSE over 2,642 observations when predictions are refreshed every

k

observations. f , Percentage of 2,634 overlapping interruption origins with lower RMSE after four rather than seven missed updates. All policies are evaluated offline on the same record.

Figure 5: Service implementation affects cost and update availability. a–c , Heat-exchanger completion, response-time p95 and mean module power for three paired 120 s blocks at 15 W automatic clocks; each offers 7,200 requests. d–f , Separate 121-observation fuel-cell replays: unavailable updates, module energy including replacement over 120.998 s, and held-field temperature RMSE at 292 withheld grid locations. Lines pair three repeats; repeated delivery sequences give one RMSE per service. The dotted line marks fresh-prediction error. Within each comparison, services share the predictor and guards but complete unequal work.

Energy-Efficient ML

Energy-efficient machine learning reduces the energy and environmental costs of training and inference while preserving useful model performance.

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William Howes, Farid Ahmed, Kazuma Kobayashi, Souvik Chakraborty+1

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Edge Computing Graph Neural Operators Spiking Neural Networks Neural Operators Virtual Sensing

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Predicting full-field physics through the real-time virtual sensing of engineering systems can enhance limited physical sensors but often requires sparse-to-dense reconstruction, complex multiphysics, and highly irregular geometries as well as strict latency and energy constraints for edge-deployability. Neural operators have been presented as a potential candidate for such applications but few architectures exist that explicitly address power consumption. Spiking neuron integration can provide a potential solution when integrated on neuromorphic hardware but the current existing neuron models result in severe performance degradation towards regression-based virtual sensing. To address the performance concerns and edge-constraints, we present the Variable Spiking Graph Neural Operator (VS-GNO) which integrates a sophisticated spectral-spatial convolutional analysis and a previously developed Variable Spiking Neuron (VSN) and energy-error balance loss function. With a non-spiking

L_2

error baseline of

0.4\%

, VS-GNO can provide a reconstruction error of

0.71\%

with

15\%

average spiking in its spectral-only form and

1.04\%

with

24.5\%

spiking in its entire form. These results position VS-GNO as a promising step towards energy-efficient, edge-deployable neural operators for real-time sparse-to-dense virtual sensing in complex, highly irregular engineering environments.

Abstract

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