TemporalFlowViz: Interactive Temporal Flow Analysis

• TemporalFlowViz is a visual analytics workflow that jointly visualizes temporal evolution, flow structures, and latent state dynamics in scramjet combustion simulations.
• It leverages image-centric preprocessing and pretrained Vision Transformers to extract high-dimensional embeddings that are clustered and mapped via UMAP and DBSCAN for effective trajectory analysis.
• The system supports interactive multi-view exploration and parameter-aware retrieval, addressing challenges like data overload, interpretive ambiguity, and cross-case comparison.

TemporalFlowViz denotes, in its explicit named usage, a parameter-aware visual analytics workflow and interactive system for making large-scale, high-dimensional temporal flow fields from scramjet combustion simulations interpretable, comparable, and communicable; in a broader research sense suggested by adjacent literature, it also names a design space in which temporal evolution, flow structure, latent state organization, and interactive interpretation are visualized jointly rather than as separate analysis stages (Jia et al., 5 Sep 2025).

1. Problem setting and analytical scope

TemporalFlowViz was introduced for scramjet combustion, a regime in which rapid, coupled interactions among shocks, turbulent mixing, and chemical reactions produce temporal flow fields that are difficult to interpret through conventional scalar summaries alone. The motivating critique is that metrics such as ignition delay and pressure rise summarize outcomes but obscure spatial–temporal phenomena such as ignition front formation, shock–flame interactions, stabilization, extinction, and re-ignition. The system is positioned against four concrete challenges: overload (C1), difficulty with rigorous interpretation of evolution (C2), lack of semantic support for knowledge sharing (C3), and difficulty of parameter-aware comparison (C4) (Jia et al., 5 Sep 2025).

The workflow operationalizes four domain requirements: latent summarization (R1), trajectory comparison (R2), semantic reporting (R3), and parameter-aware exploration (R4). Its central analytic claim is that large collections of simulation cases can be made comparable by combining compact latent representations that preserve spatial structures, clustering into latent combustion modes, embedding-space trajectories, expert-labeled centroids coupled to a vision–LLM, and parameter-aware filtering and retrieval (Jia et al., 5 Sep 2025).

This suggests that TemporalFlowViz is not reducible to a single visualization primitive. Rather, it is a compound methodology in which representation learning, interactive clustering, temporal trajectory analysis, and semantically grounded reporting are treated as mutually reinforcing components.

2. Data model, parameterization, and preprocessing

The dataset described for TemporalFlowViz comprises more than 200 scramjet combustion cases (≈3 TB of data). Each case is indexed by an initial-condition parameter vector

$$\boldsymbol{\theta} \in \mathbb{R}^p,\quad p=3,\quad \boldsymbol{\theta}=(P,\,T,\,\text{H}_2\text{O}),$$

with static pressure $P$ in [0.8, 2.1] MPa, static temperature $T$ in [565, 830] K, and water-vapor mass fraction $\text{H}_2\text{O}$ in [7.8%, 14%]. Each simulation produces a time series of frames at regular sampling intervals with dozens of frames per case, spanning fields such as static pressure, OH mass fraction, velocity, and Mach number. Domain specialists prioritized pressure for global evolution, stabilization/oscillation and OH for local combustion activity (Jia et al., 5 Sep 2025).

Preprocessing is explicitly image-centric. VTK fields were mapped to images under a uniform colormap and cropped to remove irrelevant background. The crop focuses on the isolator–cavity region where combustion phenomena manifest most strongly, and preprocessing may optionally apply spatial weighting to emphasize subregions with pronounced activity. This crop is not merely cosmetic: in a cropping study, the convergence radius—defined over the last $K$ vertices of a trajectory in PCA-reduced coordinates—was reduced by $35.24\pm0.59\%$ when focusing on the isolator–cavity region (Jia et al., 5 Sep 2025).

The convergence radius is defined as

$$r_i=\frac{1}{K}\sum_{t=T-K+1}^{T}\bigl\|p_i(t)-\overline{p_i}\bigr\|,\quad \overline{p_i}=\frac{1}{K}\sum_{t=T-K+1}^{T}p_i(t).$$

The data model therefore combines three distinct structures: a parameter vector $\boldsymbol{\theta}$, a time-indexed image sequence, and a field-specific semantic interpretation. A plausible implication is that TemporalFlowViz is best suited to settings in which temporal flow analysis cannot be separated from experimental or simulation parameterization.

3. Latent representations, clustering, and temporal trajectories

For each cropped frame, TemporalFlowViz extracts a high-dimensional embedding using pretrained Vision Transformers without fine-tuning. It supports three encoders: BLIP2-opt-2.7b, InternViT-6B-v2.5, and AIMv2-1B. The output is a per-frame embedding $\mathbf{x}_t \in \mathbb{R}^d$, with $d$ determined by the backbone. Empirically, BLIP-2 yields smooth, temporally ordered manifolds; InternViT highlights cluster separations and mode transitions; AIMv2 is noisier. Similarity is computed with Euclidean distance unless otherwise noted (Jia et al., 5 Sep 2025).

To support visual reasoning, embeddings are projected to two dimensions using UMAP or t-SNE. The reported preference is clear: UMAP better maintains local and global continuity, preserving trajectory shapes and cluster boundaries for combustion modes, and experts preferred UMAP for OH fields. Default UMAP hyperparameters are $P$0 and $P$1 (Jia et al., 5 Sep 2025).

Clustering is performed with DBSCAN, parameterized by $P$2 and $P$3. The method identifies dense regions as latent combustion modes and marks low-density points as noise. Cluster centroids are defined by

$P$4

Reported interpretations include that small compact clusters often correspond to stable scramjet, whereas larger clusters can aggregate steady ramjet. Cluster quality is assessed interactively through visual separability, trajectory continuity within clusters, consistency across similar cases, and expert verification of linked raw frames (Jia et al., 5 Sep 2025).

For each simulation $P$5 with $P$6 frames, TemporalFlowViz draws a polyline trajectory $P$7 through the latent plane. Useful trajectory metrics include speed

$P$8

and one discrete curvature option,

$P$9

with $T$0 for numerical stability. Mode transitions are detected when cluster membership changes or when speed/curvature exceed thresholds; after cropping, smoothing was not necessary given the clarity of UMAP trajectories (Jia et al., 5 Sep 2025).

The method’s epistemic structure is thus explicitly latent: combustion evolution is not visualized directly in raw field space, but through a learned manifold whose geometry is then tied back to raw frames.

4. Semantic anchoring, retrieval, and coordinated multi-view exploration

TemporalFlowViz uses domain experts to annotate representative cluster centroids with combustion-specific labels, including examples such as “stable scramjet pressure surge between isolator and cavity,” “jet-wake OH mode,” and “shear-layer OH mode.” For a cluster $T$1, the representative exemplar is chosen as the point nearest the mean,

$T$2

Two VLMs are compared—InternVL2.5-38B and Gemma‑3‑27B—and the system adopts Gemma‑3 for efficiency, specifically because it supports 4/8-bit quantization and robust multi-image batching. For a selected frame, the system retrieves the top-$T$3 nearest annotated centroids and uses them as prompt context for frame-level and case-level summaries (Jia et al., 5 Sep 2025).

Similarity-based retrieval is trajectory-aware. Analysts can filter by parameter ranges in $T$4, and case retrieval uses a Dynamic Time Warping (DTW)-based metric: $T$5 This metric is described as emphasizing late-stage behavior (convergence/stability) while allowing elastic temporal alignment. Aggregate similarity may also be computed using mean embeddings or “signatures” (Jia et al., 5 Sep 2025).

The interface is explicitly organized into coordinated views:

View	Contents	Main function
Filtering Panel	parameter sliders, case table, DBSCAN controls, field selection	subset definition
Temporal Trajectory View	2D embedding scatter, clusters, trajectories, centroid toggles	latent evolution analysis
Similar Trajectories View	top-$T$6 thumbnails by DTW-based similarity	cross-case retrieval
Details View	scrollable frame viewer for pressure/OH images	raw-field validation
Report View	expert or VLM-generated descriptions and summaries	semantic reporting

Brushing, selection, and filtering are linked across views (Jia et al., 5 Sep 2025).

The two reported case studies illustrate the interpretive role of this coordination. In Case Study 1 on pressure fields, trajectories often begin dispersed and converge into compact clusters; some cases transition from unstable scramjet to steady ramjet around ≈6 ms, whereas stable scramjet cases remain within tight clusters throughout. In Case Study 2 on OH fields, clustering separates shear-layer combustion from jet-wake combustion; even when pressure is at steady state, OH trajectories may fluctuate within a stable cluster, indicating spatial variability without mode transition (Jia et al., 5 Sep 2025).

5. Relation to adjacent temporal flow visualization research

TemporalFlowViz belongs to a wider body of work in which temporal structure, flow, and interaction are made jointly visible, although the specific mathematical objects differ substantially across domains.

System	Domain	Principal temporal object
AttentionFlow	online attention networks	influence on dynamic directed edges
FLOW portraits	widefield calcium imaging	FTLE ridges in time-varying velocity fields
HyperFLINT	scientific ensembles	interpolated scalar fields and estimated 3D flow
TimeFlow	longitudinal brain MRI	temporally conditioned deformation fields
CT-OT Flow	noisy snapshot data	reconstructed continuous-time distributions
TimeFlows	heterogeneous information objects	multi-relational process chronologies

AttentionFlow visualizes a dynamic, directed network in which each node has a univariate attention time series and each directed edge carries a time-varying influence weight. Its coordinated design combines a tree ring overview, a line chart for ego–alter comparison, and a time-aligned ego network whose node positions depend on the influencing time derived from normalized influence thresholds. The paper explicitly notes that it does not employ cross-correlation, Granger causality, or explicit lag estimation; influence is model-derived and used directly for visualization (Shin et al., 2021).

FLOW portraits transform widefield calcium imaging movies into time-varying velocity fields using Horn–Schunck optical flow, then compute finite-time Lyapunov exponent (FTLE) fields to identify repelling and attracting coherent structures. The resulting portraits summarize initiation and termination regions, dominant directions of spread, extents of propagation, and wavefronts, thereby importing Lagrangian coherent structure analysis into neuroscience (Linden et al., 2020).

HyperFLINT addresses a different but adjacent problem: ensemble-aware temporal interpolation and flow estimation for scientific data. It combines a hypernetwork conditioned on simulation parameters with a 3D interpolation-and-flow model, thereby enabling parameter-space exploration alongside interpolation at unobserved times. The paper emphasizes that its outputs can support streamlines, pathlines, LIC on slices, 3D volume glyphs, and smooth playback (Gadirov et al., 2024).

TimeFlow introduces a temporally conditioned longitudinal brain MRI registration framework in which a U-Net predicts a time-dependent deformation field $T$7 from only the baseline and endpoint scans. The paper’s visualization guidance includes time-lapse of images, vector field overlays, pathlines/streamlines, Jacobian-based volume change, and comparative panels for extrapolated future states (Jian et al., 15 Jan 2025).

CT-OT Flow addresses the inverse situation in which continuous trajectories are unavailable and data are observed only as discrete temporal snapshots with coarse or noisy timestamps. It first infers high-resolution time labels via partial optimal transport, then reconstructs a continuous-time distribution by temporal kernel smoothing, making it possible to train ODE or SDE dynamics models and to visualize evolving densities, vector fields, and streamlines (Kawano et al., 23 May 2025).

TimeFlows, despite its distinct subject matter, is conceptually relevant because it treats chronology itself as a multi-relational flow structure. It defines a heterogeneous graph over events and information objects with typed relations across TT, TE, and EE levels, including Temporal, Subject, Entity, Causal, Correspondence, Succession, References To, and Consists Of (Muller et al., 2024).

Taken together, these works suggest that “temporal flow visualization” spans at least three recurring formalizations: flow as physical transport, flow as latent trajectory evolution, and flow as directed transfer or dependency on networks. TemporalFlowViz, in the scramjet sense, occupies the second of these while remaining interoperable with the first through raw-field validation and with the third through parameter-aware comparison.

6. Limitations, interpretive cautions, and prospective directions

The TemporalFlowViz paper identifies several methodological constraints. The system is sensitive to DBSCAN/UMAP settings, and the authors note that adaptive, stability-aware tuning would improve consistency. Because the embeddings come from pretrained ViTs learned from general corpora, they may introduce biases; domain fine-tuning on combustion data is proposed to improve fidelity to ignition fronts, weak flame zones, and shock structures. Expert annotations, although effective, introduce subjectivity, motivating structured templates and collaborative validation. Reported future directions include extending to 3D volumetric data, integrating uncertainty quantification, physics-aware embeddings, interactive labeling, and event-aware trajectory segmentation (e.g., blowout/reignition) (Jia et al., 5 Sep 2025).

Related work introduces analogous cautions. In AttentionFlow, influence weights are model-derived proxies and the system does not establish causality, so analysts are warned against over-interpreting edges as causal links (Shin et al., 2021). In FLOW portraits, event alignment relies on external annotations rather than algorithmic detection, and the method cautions that low SNR, very slow frame rates, and long integration windows can degrade optical-flow and FTLE quality (Linden et al., 2020). HyperFLINT notes possible difficulty in highly turbulent regimes, shocks, or stiff source terms, and warns that extreme parameter ranges may degrade accuracy (Gadirov et al., 2024). CT-OT Flow, for its part, states that assuming a uniform observation-time law $T$8 can bias inferred velocity magnitudes when the true law is non-uniform, and that non-contiguous intervals or very high-dimensional spaces can weaken partial-transport contrast (Kawano et al., 23 May 2025).

A common misconception is that these systems directly recover ground-truth dynamics from visualization alone. The literature instead presents them as inference-and-interpretation frameworks: they expose estimated structure, organize comparison, and make temporal hypotheses inspectable, but they do not remove the need for domain validation. In that respect, TemporalFlowViz is best understood as a rigorous visual-analytic layer over learned or computed temporal representations, not as a substitute for the underlying physics, models, or expert judgment.