PMB-NN: Physiological-Model-Based Neural Network for Glucose Forecasting in Type 1 Diabetes

Yaowen Zhang; Shuhao Que; Ying Wang

physics.med-phOct 11, 2026

PMB-NN: Physiological-Model-Based Neural Network for Glucose Forecasting in Type 1 Diabetes

Authors: Yaowen Zhang, Shuhao Que, Ying Wang

Organizations: Department of Biomedical Signals and Systems, University of Twente, Enschede, The Netherlands

Abstract

Accurate, physiologically consistent glucose forecasts could help people with type 1 diabetes respond to impending excursions. We applied our physiological-model-based neural network (PMB--NN) framework to glucose forecasting. A temporal convolutional network (TCN) used 180 min of history, constrained during training by a personalized four-parameter physiological model. The main PMB--NN combined forecast and neural--physiological agreement losses; a three-term variant additionally fitted physiological predictions to measured glucose. Data comprised 6--8 weeks of continuous glucose monitoring, pump, and meal records from 25 AZT1D participants. Person-specific models used chronological 70/10/20 train/validation/test splits and 30-, 60-, and 120-min horizons. Median mean absolute errors were 16.24, 25.00, and 30.20 mg/dL with basal insulin records and 15.38, 24.21, and 31.79 mg/dL before these records became available. In the latter setting, PMB--NN had the lowest median error at 30 and 60 min; it outperformed the physiological model alone in all six settings. In input-increase tests, glucose predictions changed in the expected direction for 85% of correction boluses and 100% of carbohydrate rescues, versus 57% for active insulin and 56% for active carbohydrates. Most standalone physiological fits showed locally distinguishable parameter effects, with glucose-related coefficients more stable under resampling than insulin- or carbohydrate-related coefficients. The three-term variant improved hyperglycaemia accuracy with basal records, but did not significantly change overall MAE and reduced directional plausibility in three tests. PMB--NN combines personalized forecasting with an explicit physiological model, allowing assessment of predictive accuracy, physiological response behavior, and participant-specific coefficients.

Figures & tables

Figure 1: Workflow of the main two-term glucose PMB–NN. Data preparation produces a 36-step history of CGM, insulin, carbohydrate, derived action states, and time of day. The neural module contains three causal TCN blocks and forecasts glucose at 30, 60, and 120 min. The physiological module uses current glucose, insulin on board (IOB), and carbohydrate on board (COB) to forecast the same prediction times. The two modules are trained jointly using neural forecast-to-reference error ( $L_{f}$ ) and neural-to-PM disagreement ( $L_{c}$ ); the TCN supplies the final output. The three-term extension adds PM forecast-to-reference error ( $L_{p}$ ) with the weights specified in Eq. ( 11 ). CGM, continuous glucose monitoring; TCN, temporal convolutional network; PM, physiological model; PMB–NN, physiological-model-based neural network; $G_{b}$ , glucose operating point; $k_{G}$ , return rate; $S_{I}$ , insulin-response coefficient; $k_{\mathrm{carb}}$ , carbohydrate-response coefficient.

Context	Horizon	PMB–NN	TCN	GRU	LSTM	Transformer	PM
Basal	30	16.24	16.23	15.81	17.52	16.03	18.89 ∗
Basal	60	25.00	23.66	23.00	24.41	24.27	28.01 ∗
Basal	120	30.20	30.46	30.32	31.18	30.12	33.53 ∗
No basal	30	15.38	16.65 ∗	17.32 ∗	18.90 ∗	18.65 ∗	16.60 ∗
No basal	60	24.21	24.46 ∗	24.77 ∗	25.23 ∗	26.10 ∗	25.72 ∗
No basal	120	31.79	31.26	32.93	30.73	31.54	33.23 ∗

Table 1: Median test mean absolute error (MAE, mg/dL) across participants. Bold marks the lowest median in each row. An asterisk indicates significantly higher comparator error than PMB–NN in a paired two-sided Wilcoxon signed-rank test with Holm correction within each context–horizon setting (

p_{\mathrm{Holm}}<0.05

). PMB–NN, physiological-model-based neural network; TCN, temporal convolutional network; GRU, gated recurrent unit; LSTM, long short-term memory; PM, standalone physiological model.

Figure 2: Numerical accuracy of the two-term PMB–NN

Figure 3: Physiological plausibility of the two-term PMB–NN and comparator models under controlled input changes. (a–d) Median changes in 60-min forecasts after increasing IOB, COB, a correction bolus at glucose

\geq 180

mg/dL, or rescue carbohydrate at glucose

\leq 80

mg/dL. Insulin should decrease or leave unchanged the forecast; carbohydrate should increase or leave it unchanged. (e) For each input-change type, the median fraction of eligible test windows with the expected response at the largest dose, summarized across participants, contexts, and horizons. A fraction of 1 indicates that all tested forecasts followed the expected direction. (f) Median 30-min MAE across contexts versus the arithmetic mean of the four model-specific fractions in (e). The upper-left direction represents lower error and more consistent responses. The dashed line joins models for which no displayed comparator has both lower error and higher mean direction plausibility. IOB, insulin on board; COB, carbohydrate on board; MAE, mean absolute error; PMB–NN, physiological-model-based neural network; TCN, temporal convolutional network; GRU, gated recurrent unit; LSTM, long short-term memory; PM, standalone physiological model.

Parameter	Unit	Basal	No basal
$G_{b}$	mg/dL	167.73 [148.87–174.57]	156.24 [146.08–166.97]
$k_{G}$	min -1	0.00882 [0.00757–0.01000]	0.00752 [0.00685–0.00884]
$S_{I}$	mg/dL/min/U	0.0776 [0.0615–0.0836]	0.0854 [0.0699–0.0967]
$k_{\mathrm{carb}}$	mg/dL/min/g	0.02282 [0.01849–0.02984]	0.01932 [0.01548–0.02478]

Table 2: Personalized effective physiological parameters estimated by the main two-term PMB–NN. Values are participant median [interquartile range].

G_{b}

, glucose operating point;

k_{G}

, glucose return rate;

S_{I}

, IOB-based glucose-lowering coefficient;

k_{\mathrm{carb}}

, COB-based glucose-raising coefficient.

Figure 4: Reliability diagnostics for the physiological parameters. Of 49 independent participant–context PM fits, 47 had numerical rank four, i.e., all four parameter effects were locally distinguishable; the other two had rank three. (a) Normalized singular-value spectra of the independent-PM sensitivity Jacobians; thin lines show individual fits and thick lines show context medians. The indices denote directions formed by combinations of scaled parameters, not individual parameters. (b) Condition numbers for the 47 rank-four fits (24 basal and 23 no-basal); black segments and open circles indicate the interquartile range and median. (c) Cumulative distributions of parameter CV from 24-h block-bootstrap PM refits; the dotted line marks CV

=0.5

. (d) Fractions with CV

<0.5

(upper rows) and fractions of PMB–NN estimates within the independent-PM 95% bootstrap intervals (lower rows). The latter indicate estimator agreement, not PMB–NN interval coverage. (e) PMB–NN parameter percentiles compared between recording contexts, with Spearman correlations. (f) Relationship between Jacobian conditioning and median parameter CV for the same 47 rank-four fits used in (b). CV, coefficient of variation; CI, confidence interval; PM, physiological model; PMB–NN, physiological-model-based neural network.

Figure 5: Comparison of the main two-term PMB–NN (

L_{f}+L_{c}

) and three-term extension (

L_{f}+0.5L_{c}+L_{p}

). (a) Distributions of paired overall MAE changes, defined as three-term minus two-term. Negative values favor the extension. (b) Paired MAE changes for basal-context targets with observed glucose above 180 mg/dL (hyperglycaemia). (c) Median paired changes in direction-plausible fractions at the largest input doses; negative values indicate lower plausibility in the extension. Circle area represents difference magnitude; blue indicates a decrease and red an increase. In (b,c), asterisks indicate Holm-adjusted

p<0.05

. (d) Distributions of epoch-mean gradient cosine similarities; negative values indicate opposing updates within the specified parameter space. (e) Between-formulation Spearman correlations of participant parameter rankings with approximate 95% intervals. B, basal context; NB, no-basal context; 2L, two-term; 3L, three-term;

L_{f}

, neural forecast-to-reference loss;

L_{c}

, neural-to-PM consistency loss;

L_{p}

, PM forecast-to-reference loss; MAE, mean absolute error; PMB–NN, physiological-model-based neural network.

Calibration	30 min	60 min	120 min
1 day	27.17 [18.81–38.03] ∗	34.37 [26.87–51.26] ∗	42.41 [31.16–55.90] ∗
3 days	20.61 [16.98–24.47] ∗	29.69 [25.62–34.88] ∗	36.59 [32.01–47.91] ∗
6 days	19.12 [16.57–22.29] ∗	28.03 [24.60–31.54] ∗	32.90 [30.18–41.34] ∗
10 days	19.05 [16.85–21.19] ∗	27.40 [24.89–32.47] ∗	35.96 [29.95–40.16] ∗
15 days	18.29 [15.67–20.67] ∗	25.84 [23.39–30.16] ∗	33.13 [26.90–40.39] ∗
Full protocol	16.24 [13.72–17.77]	25.00 [21.72–27.50]	30.20 [27.06–37.25]

Table 3: Basal-context test MAE (mg/dL) after short-duration calibration of the main two-term PMB–NN. Values are participant median [interquartile range] for the same 25 participants and test windows. An asterisk indicates higher error than the full protocol in paired two-sided Wilcoxon tests with Holm correction over the 15 duration–horizon comparisons (

p_{\mathrm{Holm}}<0.05

). The full protocol used the original 70% training and 10% validation partitions; its pre-test period had a median duration of 22.2 days (range 20.5–22.5). Short-duration fits retained the final epoch, and the full protocol used validation-selected checkpoints. MAE, mean absolute error; PMB–NN, physiological-model-based neural network.

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Accurate long-horizon glucose forecasting is critical for automated insulin delivery systems, which help people with type 1 diabetes (T1D) manage their glucose and avoid dangerous hypoglycemia. However, standard recursive long short-term memory (LSTM) networks suffer from systematic negative bias at longer horizons due to error compounding, while purely mechanistic ordinary differential equation (ODE) models fail to generalize across individuals when parameterized at the population level. We propose PhysioSeq2Seq, a hybrid architecture that combines patient-specific physiological modeling with a sequence-to-sequence (Seq2Seq) LSTM. For each glucose segment, twin matching searches a population of 300 parameterized digital twins to identify the best-fitting physiological match from a 3-hour continuous glucose monitoring (CGM) history. The 10 internal ODE state variables of the matched twin are injected as exogenous covariates into both the encoder and decoder of the Seq2Seq LSTM. This simultaneous 48-step prediction strategy eliminates recursive error compounding, while the ODE features provide a physics-grounded constraint that bounds long-horizon drift within physiologically plausible ranges. PhysioSeq2Seq was trained on CGM and insulin data from 348 participants in the Type 1 Diabetes Exercise Initiative (T1DEXI) dataset and evaluated on 74 held-out participants. At the 240-minute horizon, PhysioSeq2Seq achieves a mean absolute error of 39.28 mg/dL and a mean error of -10.62 mg/dL, reducing bias by 13.89 mg/dL over the recursive LSTM and reducing mean absolute error by 28.62 mg/dL over the ODE-based digital twin. These results show that eliminating architectural feedback and injecting patient-matched physiological states is an effective and clinically meaningful strategy for long-horizon glucose forecasting in T1D.

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