Findings

Results

Six new architectures against two shared baselines, on 32 South African weather stations, out to 48 hours — reported workstream by workstream.

How to read this page

All three workstreams share the dataset, the chronological split, the preprocessing, the training loss and the 48-hour horizon, and all three measure against the same two baselines. They do not share the number of random seeds, the input regime, or the full metric set, because each workstream's research question demanded something different.

Results are therefore reported per workstream, against the shared baselines — the comparison each study actually ran. Numbers are not merged into a single ranking across workstreams, because the differing seed budgets and input regimes mean a cross-workstream difference of a few percent cannot be attributed to the architecture.

Where this matters in practice. The continuous-time and diffusion workstreams agree closely on AGCRN — 2.197 °C and 2.194 °C average temperature MAE, computed independently. They differ on CLCRN (2.410 against 2.146 °C) because one CLCRN run out of the continuous-time workstream's ten temperature seeds failed to converge and was deliberately retained in the reported mean rather than discarded. Excluding that run, the two agree on CLCRN as well. The divergent run is discussed in the continuous-time workstream; it is a reliability finding, not a discrepancy to be smoothed over.

**Protocol by workstream.** Everything not listed here is shared — see the shared experimental setup. An em dash marks a value the source does not state.
	Continuous-time	Diffusion-based	Lightweight
Student	Praise Jaravani	Génevieve Chikwanha	Zoleka Fuyana
Challengers	MTGODE, STGODE	DiffSTG, USTD	STLGRU, LiteSTGNN
Random seeds	10 (42–51)	3 (2024, 2025, 2026)	—
Input regime	all six variables in, one target out	univariate per variable	—
Point metrics	MAE, RMSE, NRMSE	MAE, RMSE	MAE
Additional metrics	valid forecast horizon; PR-AUC, F1, CSI for extreme-event detection	CRPS for probabilistic forecasts	parameter count, inference cost
Extra analyses	extreme-stratified error, 2×2 factorial design, named heatwave case study, seed stability	exogenous-covariate ablation, spatial and elevation error patterns, learned adjacency maps	capacity–accuracy trade-off
Hardware	NVIDIA L40S	NVIDIA A100	—

Workstream 1

Continuous-time: MTGODE and STGODE

Four architectures, crossing the spatial prior (learned adaptive graph against geometric construction) with the temporal formulation (discrete recurrence against continuous-time neural ODE). Ten seeds per cell; 190 runs across the campaign.

**Test MAE by forecast lead**, means over ten seeds, in physical units. Lowest model per row in bold. Persistence holds the last observed value; climatology predicts the training-period mean.
Lead	AGCRN	CLCRN	MTGODE	STGODE	Persist.	Clim.
Temperature (°C)
3 h	1.417	1.711	1.284	1.470	2.953	5.002
6 h	1.730	1.983	1.640	1.864	5.168	5.002
9 h	1.844	2.095	1.789	1.978	6.574	5.003
12 h	1.886	2.143	1.848	1.991	7.064	5.005
24 h	2.181	2.402	2.102	2.226	2.821	5.005
48 h	2.713	2.910	2.623	2.702	3.462	5.007
Average	2.197	2.410	2.108	2.256	5.318	5.005
Surface pressure (hPa)
3 h	2.049	1.845	1.252	1.587	1.295	7.749
6 h	2.434	2.183	1.702	2.169	2.080	7.749
9 h	2.753	2.467	2.219	2.557	2.493	7.749
12 h	3.051	2.765	2.692	2.873	2.877	7.749
24 h	4.207	3.954	4.059	4.158	4.133	7.750
48 h	5.365	5.279	5.464	5.383	5.506	7.754
Average	4.042	3.817	3.818	3.948	4.005	7.750
Relative humidity (%)
3 h	6.570	6.263	6.006	6.588	11.078	19.000
6 h	8.003	7.648	7.560	8.328	18.983	19.000
9 h	8.619	8.244	8.243	8.964	24.111	18.998
12 h	8.931	8.587	8.579	9.230	26.044	18.996
24 h	10.014	9.709	9.660	10.273	12.742	18.999
48 h	11.493	11.337	11.233	11.673	14.673	18.995
Average	9.842	9.527	9.454	10.075	20.361	18.997
Wind speed (m s⁻¹)
3 h	0.894	0.879	0.855	0.901	1.099	1.497
6 h	1.037	1.004	0.989	1.061	1.550	1.497
9 h	1.102	1.057	1.048	1.124	1.820	1.497
12 h	1.124	1.083	1.076	1.142	1.935	1.497
24 h	1.178	1.149	1.139	1.184	1.476	1.497
48 h	1.227	1.213	1.203	1.227	1.558	1.497
Average	1.149	1.120	1.110	1.157	1.721	1.497

MTGODE attains the lowest horizon-averaged error on temperature, relative humidity and wind speed, and is statistically inseparable from CLCRN on surface pressure. Against the naive baselines the improvement divides sharply by variable: every model reaches roughly half of the better baseline's error on temperature and humidity and about three quarters on wind speed, but on surface pressure the four barely improve on persistence at all.

Four log-scale line charts of test MAE against forecast lead from 1 to 48 hours, for temperature, surface pressure, relative humidity and wind speed. The four model curves lie close together and converge as lead increases; the persistence baseline shows a pronounced diurnal sawtooth. — **Error against forecast lead.** Log axes, means over ten seeds. The spread between architectures is widest at short lead and largely gone by two days. Persistence's diurnal sawtooth is visible — the models stay below it even at its minima, so they capture more than the daily cycle. Figure 4, Jaravani (2026).

Four interaction plots, one per variable. In each, the line for the learned adaptive graph slopes downward from discrete to continuous time while the line for the geometric prior slopes upward, so the two lines cross. — **The lines cross on every variable.** Moving from a discrete to a continuous-time formulation *lowers* error under a learned adaptive graph (AGCRN → MTGODE) and *raises* it under a geometric prior (CLCRN → STGODE). The interaction is negative on all four variables, from −3.3% to −5.2% of the four-cell mean, and exceeds either design axis on its own. Figure 5, Jaravani (2026).

Behaviour on extremes

**Extreme-stratified test MAE** — error on hours exceeding the station's training 95th percentile, against all other hours, with the degradation factor in brackets. Means over ten seeds.
Model	Temperature (°C)	Pressure (hPa)	Humidity (%)	Wind speed (m s⁻¹)
AGCRN	3.77 / 2.11 (1.79)	7.50 / 3.66 (2.05)	9.97 / 9.82 (1.02)	3.54 / 1.06 (3.35)
CLCRN	4.61 / 2.29 (2.02)	6.87 / 3.48 (1.97)	9.37 / 9.53 (0.98)	3.51 / 1.03 (3.42)
MTGODE	4.02 / 2.00 (2.01)	7.65 / 3.41 (2.24)	9.54 / 9.44 (1.01)	3.46 / 1.02 (3.40)
STGODE	4.01 / 2.16 (1.86)	7.63 / 3.55 (2.15)	10.24 / 10.04 (1.02)	3.69 / 1.06 (3.49)
Persistence	8.83 / 5.12 (1.72)	6.74 / 3.79 (1.78)	18.54 / 20.54 (0.90)	4.22 / 1.63 (2.58)
Climatology	13.16 / 4.55 (2.89)	18.30 / 6.58 (2.78)	31.78 / 17.58 (1.81)	4.69 / 1.37 (3.41)

How far error grows in the tail is set by the variable, not the architecture — steep on wind speed, moderate on temperature and pressure, and absent on relative humidity, whose upper tail is a bounded saturation region where variance compresses rather than expands. Critically, the pooled ordering does not survive stratification on three of four variables: a discrete-recurrence model holds the lowest extreme-regime error on temperature, pressure and humidity, while MTGODE — lowest on average — leads the tail only on wind speed.

**Extreme-event detection**, PR-AUC and ROC-AUC per label variable, means over ten seeds. Labels are exceedances of a 95th percentile conditioned on station, day-of-year and hour-of-day, so a classifier that knows only the calendar has no advantage. Best in bold.
Model	Temperature		Precipitation		Humidity		Wind speed
	PR	ROC	PR	ROC	PR	ROC	PR	ROC
AGCRN	.167	.729	.020	.754	.215	.662	.096	.674
CLCRN	.205	.769	.026	.794	.235	.696	.110	.690
MTGODE	.218	.780	.026	.796	.254	.716	.132	.720
Persistence	.106	—	.006	—	.165	—	.057	—
Seasonal climatology	.061	—	.006	—	.093	—	.035	—
Base rate (prevalence)	.065	.500	.007	.500	.117	.500	.043	.500

Full continuous-time workstream →

Workstream 2

Diffusion-based: DiffSTG and USTD

Two probabilistic diffusion models against the same two deterministic baselines, with CRPS added to assess the quality of the predictive distribution rather than only the point forecast. Three seeds per cell; the diffusion models produce eight samples per run, averaged for comparison with the baselines.

**Average forecasting performance** across all stations and horizons, mean ± standard deviation over three seeds. Best per column in bold.
Model	Humidity (%)		Pressure (hPa)		Temperature (°C)		Wind speed (m s⁻¹)
	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE
AGCRN	9.923	13.974	4.340	10.470	2.194	3.019	1.125	1.604
CLCRN	9.519	13.231	3.883	8.857	2.146	2.907	1.122	1.580
DiffSTG	11.137	14.883	6.369	13.904	2.372	3.183	1.170	1.650
USTD	9.965	13.867	4.329	9.117	2.209	2.974	1.151	1.647

CLCRN is the best point forecaster on every variable and metric. DiffSTG is the worst on every variable and metric — its pressure MAE is roughly 47% higher than USTD's and 64% higher than CLCRN's. USTD is the competitive one: it tracks AGCRN within 3% on MAE for every variable, and beats it by 12.9% on pressure RMSE.

The gap between the two diffusion models is the finding. Both are diffusion models and both are non-autoregressive, so neither property explains the difference. What separates them is conditioning: USTD puts a deterministic spatio-temporal encoder in front of the diffusion transformer, so denoising operates on a representation that has already captured conditional structure, and it conditions on time of day, day of year and station height.

Four line charts of RMSE against forecast horizons of 3, 6, 9, 12, 24 and 48 hours for humidity, pressure, temperature and wind speed, comparing CLCRN, AGCRN, DiffSTG and USTD. All curves rise with horizon; DiffSTG is consistently highest. — **RMSE across forecast horizons.** All models degrade as lead grows. DiffSTG produces the highest error at every horizon on every variable; USTD and AGCRN give the lowest errors at short lead, with CLCRN and AGCRN generally ahead between 6 and 24 hours. All four converge by 48 hours. Figure 3, Chikwanha (2026).

Four grouped bar charts showing USTD's MAE and RMSE for temperature, pressure, humidity and wind speed under three conditions: all exogenous variables, time of day only, and no exogenous variables. Error rises as covariates are removed, most sharply for pressure. — **Ablation: what the covariates are worth.** Removing all exogenous variables raises USTD's RMSE from 2.974 to 3.411 on temperature, 13.867 to 14.523 on humidity, 1.647 to 1.737 on wind speed — and from 9.117 to 13.230 on pressure, a 45% deterioration. Contextual information, not the diffusion formulation, is doing much of the work. Figure 2, Chikwanha (2026).

**Probabilistic performance (CRPS)**, averaged over the test set. Lower is better. CRPS scores the whole predictive distribution, where MAE and RMSE score only a point.
Variable	DiffSTG	USTD	Better
Surface pressure	0.0060	0.0043	USTD
Temperature	0.1076	0.1045	USTD
Relative humidity	0.1266	0.1219	USTD
Wind speed	0.3745	0.4073	DiffSTG

USTD achieves both lower point error and lower distributional error on three of four variables. Wind speed is the exception and is instructive: USTD's samples are visibly more dispersed there and its MAE is slightly lower, yet its CRPS is worse — so sample spread is not itself a measure of uncertainty quality. Whether dispersion helps depends on how well the resulting distribution matches the observations.

Full diffusion workstream →

Workstream 3

Lightweight: STLGRU and LiteSTGNN

The lightweight workstream asks what the parameter budget actually buys. Its headline result is that adding capacity to a small model gives sharply diminishing returns: STLGRU is 4.1× the size of LiteSTGNN and improves MAE by only 0.7–5.7%. Performance was competitive with the baselines but variable-dependent — which family wins depends on which variable is being forecast. On surface pressure both lightweight models sit clearly below AGCRN and CLCRN; on temperature and relative humidity the baselines lead; on wind speed the four are near-indistinguishable. The per-horizon curves are on the workstream page.

This is the same pattern the continuous-time workstream found from the opposite direction, where the most accurate model of four was also among the cheapest, at 138,096 parameters against 1,663,104 for the weakest, and CLCRN, the smallest of the four, separated from the far larger STGODE on every variable. Across both workstreams, model size and model accuracy are close to unrelated on this dataset.

Full lightweight workstream →

What holds across all three

Four patterns appear across the workstreams, despite the different architectures, metrics and seed budgets.

1 · The variable matters more than the architecture

Error growth with lead time, the size of the gap to the naive baselines, and the degradation on extremes are all set far more by which variable is being forecast than by which model is forecasting it. The spread between architectures is 4–6% of the mean on most variables; the spread between variables is much larger. Station difficulty, likewise, is a property of the site: the four continuous-time models rank the 32 stations near-identically, with per-station error correlations of 0.98 to 1.00.

2 · Models converge by 48 hours

Whatever separates the architectures at short lead has largely disappeared by two days. On surface pressure the spread falls from 47.3% of the mean near the first lead to 3.5% at 48 hours. A ranking established at the previous studies' 24-hour ceiling does not straightforwardly extend past it.

3 · Surface pressure is the hard case

It is the variable where the learned models struggle most to beat persistence — at the shortest lead every model's pressure error is 1.8 to 3.5 times persistence's, and the four only overtake it by two days. It is also where the models disagree most with one another, where seed-to-seed variation is highest, and where the exogenous-covariate ablation bites hardest. Altitude spread across the network is the likely common cause.

4 · Conditioning beats paradigm

In both the continuous-time and diffusion workstreams, the within-family gap was larger than the family-versus-baseline gap, and in both cases the explanation was how the model is conditioned on space and context — a learned graph against a geometric one, a deterministic encoder with covariates against raw diffusion. Adopting a new paradigm is not what improves a forecast; conditioning it well is.

← Background Continuous-time workstream →