ETGS: Explicit Thermodynamics Gaussian Splatting for Dynamic Thermal Reconstruction
Authors: Zhongwen Wang
Han Ling
Weihao Zhang
Yinghui Sun
Quansen Sun
Venue: ICLR 2026 Poster (2026)
Keywords: 3D Reconstruction; Thermal Reconstruction; Explicit Thermodynamics
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: We propose ETGS, a method for reconstructing dynamic thermal scenes by embedding explicit thermodynamic modeling into 3D Gaussian Splatting. Each Gaussian is equipped with physically interpretable thermal parameters, and its thermodynamics evolution is described by a first-order heat-transfer ODE with an analytical closed-form solution. This formulation avoids numerical integration, enables efficient rendering at arbitrary timestamps, and naturally handles irregular sampling and out-of-order observations. We also introduce the Rapid Heat Dynamics (RHD) dataset, which provides millisecond-aligned RGB–IR image pairs covering typical thermal processes such as cooling, warming, heating, and heat transfer. Experiments on RHD show that ETGS captures rapid thermal dynamics more accurately than existing static and dynamic baselines, while maintaining training and rendering efficiency close to that of static 3DGS. Code and dataset are available at https://github.com/jankin-wang/ETGS.

Published as a conference paper at ICLR 2026
ETGS: EXPLICIT THERMODYNAMICS GAUSSIAN SPLATTING FOR DYNAMIC THERMAL RECONSTRUC- TION
Zhongwen Wang', Han Ling Weihao Zhang Yinghui Sun Quansen Sun
Nanjing University Science and Technology, "Southeast University
[jankinwang, 321106010190, zhangweibao, junquansenJenjjst. .dd.. en, sunyh@seu. on
3DGRK 594 (ee) Tnin 141x, 29.2
Mie-Splutireg 205 (ie)
DD-GOES foil
NTR Gaus i3 Gpa
4DGS 284 (je Trater 1o0 P5.
Ound458 fpe) Unin 184s PSNN.3
Teain: 1874,
Trin 1005.
Ground Truth
PSNR:29.
PSNR-35
Figure I: Our method achieves high-quality rendering of dynamic thermal scenes with efficiency comparable to static methods (Kerbl et al. (2023); Yu et al. (2024)). The key to this performance the novel explicit modeling of dynamic thermal Gaussians based on thermodynamics, which sig- nificantly speeds up scene optimization and synthesis of new views, while achieving state-of-the-an quality.
ABSTRACT
We propose ETGS, a method for reconstructing dynamic thermal scenes by em- bedding explicit thermodynamic modeling into 3D Gaussian Splatting. Each Gaussian is equipped with physically interpretable thermal parameters, and its thermodynamies evolution is described by first-order heat-transfer ODE with analytical closed-form solution. This formulation avoids numerical integration, enables efficient rendering at arbitrary timestamps, and naturally handles irregular sampling and oft-of-order observations. We also introduce the Rapid Heat Dy- namics (RHD) dataset, which provides millisecond-aligned RGB-IR image pairs covering typical thermal processes such as cooling, warming, heating, and heat transfer. Experiments ics more accurately than existing static and dynamic baselines, while maintaining training and rendering efficiency close that of static 3DGS. Code and dataset are available at https: / thub com/ jank wwnng /aTan//ETSS
RHD show that ETGS captures rapid thermal dynam-
INTRODUCTION
Thermal imaging is non-contact temperature measurement method that can directly capture ther- mal radiation signals from an object's surface and maintains stable operation even in complex en- vironmental conditions such as low light levels (Wilson et al. (2023); Li et al. (2024a); Xu et al. (2025); Shin & Park (2025)). Compared traditional visible light imaging, thermal imaging only provides geometric structural information but also reflects the temperature distribution char- acteristics of an object, thus demonstrating unique advantages 3D scene modeling and physical process analysis (Aibibu et al. (2025); Nowakowski & Kaczmarek (2025); Wang et al. (2025); Wu al. (2020); Ramon al. (2022)). Therefore, combining thermal imaging with 3D reconstruction
"Corresponding author.

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Published as a conference paper at ICLR 2026
to generate temperature scene models that evolve over time has become research hotspot in recent years.
Neural Radiance Fields (NeRF) (Mildenhall et al. (2021)) uses implicit neural networks to model seenes, producing high-quality results in novel perspective synthesis tasks. In thermal scene mod- eling, Thermal-NeRF (Ye et al. (2024)) and ThermoNeRF (Hassan al. (2024)) extend NeRF to IR images, achieving 3D temperature field reconstruction. However, NeRF"s implicit representation suffers from geometric instability and inefficiencies in training and rendering (Wang al. (2024); Li et al. (2023; 2024b); Korhonen et al. (2024)), making it difficult to implement in dynamic scenes. Unlike NeRF, 3D Gaussian Splatting (3DGS) (Kerbl et al. (2023)) uses explicit Gaussians to model scenes, and all parameters (position, size, orientation, color, etc.) can be learned, resulting in strong scalability and downstream compatibility (Fei al. (2024); Charatan et al. (2024); Tang Cham (2024)). Recently, methods such as Thermal3D-Gr (Chen et al. (2024)) and TGA-GS (Zou et al. (2025)) have introduced 3DGS into thermal reconstruction tasks, achieving 3D modeling and per- spective synthesis of thermal scenes. However, they are all limited to static scenarios and fail to capture the dynamic process of temperature change over time, so they have obvious limitations in thermodynamic analysis.
To address dynamics, some work has introduced temporal modeling on 3DGS. 4DGS (Wu et al. (2024)) incorporates temporal variables into the Gaussian representation, enabling it to reconstruct dynamic appearances, but does not consider thermophysical processes. ThermalGS (Liu et al. (2025)) attempts to drive the temporal evolution of the Gaussian through temporal embedding and semantic information, but is essentially still data-driven modeling and lacks thermodynamic consis- tency.
(Yang al. (2025)) introduces thermodynamic equations into the Gaussian framework, but it relies on implicit neural networks and integral inference, which limits its training and rendering efficiency.
To address these limitations, we propose ETGS, a reconstruction method for dynamic thermal scenes based on explicit thermodynamic modeling. We directly introduce explicit thermal physical vari- ables into the Gaussian representation and derive the closed-form solution of the ordinary differen- tial equation (ODE) at arbitrary time, avoiding the overhead of numerical integration and naturally adapting to unequal sampling and disordered timestamps. By combining explicit thermodynamic modeling with the Gaussian rendering framework, the proposed method close to static 3DGS in training and inference efficiency, while achieving significantly better performance than recent state-of-the-as baselines in dynamic thermal reconstruction tasks. In addition, we also constructed an RHD dataset that covers typical processes such warming, cooling, heating and heat transfer, and provides millisecond timestamps and pixel-aligned RGB-IR data, thus laying the foundation for quantitative research dynamic thermal scenes. Our contributions are summarized follows:
We propose a dynamic thermal scene reconstruction method based on explicit thermo- dynamic physics. We construct reliable thermodynamic model using equivalent heat capacity, heat exchange coefficients, and heat source excitations. We derive closed-form solutions to ODEs at arbitrary time, enabling efficient rendering under unequal sampling and oft-of- sampling.
We introduce the Rapid Heat Dynamics (RHD) dataset, a new dataset designed specifically for rapidly changing thermal dynamics. It covers the thermodynamic processes of warming, cooling, heating, and heat transfer, along with millisecond timestamps and pixel- aligned RGB data.
Experimental results demonstrate that the proposed method reliably reconstructs rapidly changing thermal dynamics with comparable training and rendering efficiency to static 3DGS, and outperforms existing methods across various metrics.
RELATED WORK
2.1 3D THERMAL SCENE RECONSTRUCTION
3D thermal scene reconstruction aims to recover both scene geometry and thermal radiation, sup- porting applications such as energy efficiency monitoring, industrial inspection, and medical diag- nosis (He et al. (2021); Glowacz (2021); Lahiri et al. (2012); Zhou et al. (2021)). Early methods
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Timaron (0) = Tur + Teco 1/11
Dynamic Thermal Scene
Gaussian Temperature
Gaussian Temperature
Time
Ru(0) - Au sin(ae + B1 con(on
Time
MM +
0,
My Stn(ou,) Big cos(se,e)
Time
Trajectory
Time (6)
Cameras
Ex
(22() A sin(ost) Bu cos(one)
2:(0) Trmma ((t)
C,
- Trlddds
Fo
Time (())
Time (6)
Figure 2: Method Overview. ETGS directly incorporates thermal physics modeling into the explicit Gaussian scene representation. The temperature of each Gaussian consists of two components: an exponential term (7 (Neetonn) that follows Newton's 's law of cooling, describing its equilibrium tendency with the ambient temperature; and a heat source excitation term (Q) expanded by a set of harmonic functions, representing periodic or complex external energy inputs. These two components combine to form a temperature evolution model.
adopted a two-stage strategy: reconstruct 3D structure from RGB images and then map thermal images (Dlesk et al. (2022); Jia et al. (2017); Zhao et al. (2017)). While feasible, these methods underuse thermal information and are restricted to static settings.
Recent works explore neural implicit models. NeRF (Mildenhall al. (2021)) has been extended to thermal imaging, e.g., ThermoNeRF (Hassan et al. (2024)) and Thermal-NeRF (Ye et al. (2024)), which learn 3D thermal distributions and synthesize novel views. However, implicit NeRFs suffer from unstable geometry and high training/rendering cost, limiting scalability to large or dynamic scenes.
Different from NeRF, 3D Gaussian Splatting (3DGS) (Kerbl et al. (2023)) adopts explicit Gaussians for efficient rendering and editability. Extensions such Thermal3D-GS (Chen et al. (2024)) and TGA-GS (Zou et al. (2025)) apply 3DGS to thermal modeling, achieving faster rendering but still constrained static scenes, thus failing capture temporal temperature evolution.
2.2 DYNAMIC RECONSTRECTION AND THERMODYNAMICS MODELING
To model dynamics, 4DGS (Wu et al. (2024)) extends Gaussians with deformation fields to capture geometry and appearance changes; follow-ups further improve efficiency (Wan et al. (2024); Lee et al. (2024); Zhang al. (2025); Li et (2024c)). Yet, these methods address only appearance, not thermal physical properties, and are unsuitable for thermal dynamic scenes. ThermalGS (Liu et al. (2025)) introduces time embeddings for dynamic thermal modeling. but remains data-driven and prone to physical inconsistency. NTR-Gaussian (Yang et al. (2025)) incorporates thermodynamic parameters via neural prediction and numerical integration, improving physical fidelity but at high computational cost due its implicit representation.
In contrast, our method directly embeds thermophysical parameters into Gaussian primitives and de- rives closed-form, differentiable time solutions. This design avoids numerical integration, maintains efficiency comparable to static 3DGS, and yields physically consistent dynamic thermal reconstruc- tions.
METHOD
We present Explicit Thermal Gaussian Splatting (ETGS), which embeds thermophysical modeling into explicit Gaussian representation. Each Gaussian carries geometry and time-evolving tem- perature state governed by two components (Fig. 2): an exponential term from Newton's 's cooling toward ambient equilibrium, and heat source excitation expanded harmonic bases capture
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periodic/complex inputs. Their combination yields closed- differentiable temperature lution that can be evaluated at any timestamp- -itthut without numerical integration or implicit neural re- -herrryy naturally handling unequal and out-of-order sampling. This design attains train- ing/rendering efficiency close to static 3DGS while accurately reconstructing fast thermal dynamics, striking balance among accuracy, efficiency, and physical plausibility.
3.1 THERMAL GAUSSIAN FIELD
In 3DGS, scene is an explicit Gaussian field of millions of parameterized Gaussians G,. Its basic form is:
G: = (us, Ei, Rí, oi, Jit,
where 14, E R represents the center position of Gaussians, Σ, represents the covariance matrix, R represents the rotation matrix, a; represents the opacity, and fi represents the characteristic coeffi- cient related to color radiation (represented in the form of spherical harmonic function expansion). This explicit representation makes 3DGS efficient and flexible in geometry and appearance model- ing. However, for thermal scenes, the various properties of the Gaussians need to be redefined. As the determining factor of thermal radiation, temperature is necessary to be explicitly represented
in modeling. To this end, we expand the Gaussians G2 into thermal Gaussians G2 and remove the optical properties (spherical harmonic color) focus on thermal reconstruction. The definition of thermal Gaussians is:
(2) New thermal properties include: equivalent heat capacity C₁ which characterizes the inertia of the Gaussians to temperature changes and determines how quickly the temperature responds to external stimuli; heat transfer coefficient hu, which describes the rate of heat exchange between the Gaus- sian body and the environment; heat source excitation Qi(I). which represents the energy input to the thermal Gaussians over time and expanded using a set of Fourier basis functions char- acterize complex or periodic thermal processes; and temperature state (t),, which represents the temperature of the thermal Gaussians at time and is analytically solved by a thermodynamic evo- lution model (see Section 3.2). This design preserves the explicit controllability of the scene and lays the foundation for physically consistent and efficient rendering of subsequent dynamic thermal processes.
G = {14 E,, R4, a,, C2 h4 (tt)).
3.2 THERMODYNAMIC EVOLUTION
This section details the thermodynamic evolution of thermal Gaussians, including the first-order linear differential equations and their analytical solutions, derived from Newtonian heat exchange and heat source excitation, and the closed-form solution obtained after expanding the heat source Q+(t) over global frequency grid using harmonic basis.
Continuous ODE model. For the i-th thermal Gaussian, assume the environment temperature is a constant Ten., the equivalent heat capacity C 0, the convection/rudiation equivalent heat transfer coefficient h; 2 0, and the heat source is (t). Based on the energy conservation principle, the first-order linear ODE is obtained:
C; d'i((t
= h4 (T.(f) - Tenw) + (tt)).
(3)
dt
Defining the time constant
C. Eq. 3 can be rewritten
h
dfi(t) 1 (T:(1) Tenu) Qi(1) C2
(4)
di Tj
Analytical solution of the ODE, Applying the integrating factor method to Eq. 4 (see Appendix A for the detailed derivation) and denoting the initial condition by T,(0) T,o. we obtain:
Tt(t)= = Tenv + (Ti, Tenw) e 1 I.5
- Q.(s)ds.
C.Jo
(5)
Harmonic expansion of the heat source. We expand the heat source on a globally shared frequency grid:
K
(i(t) = Σ
Asasin (wat) + Bi, (wat).
(6)
k=
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where {wx J sampled from log -niform frequency grid:
Wmax
Wk
Wmin
K-1
d 1, 1,..., K.
Wmin
The bounds [wimin Wmax] and the number of frequencies K are jointly determined by the sampling geometry (observation duration Tspan minimum sampling interval dtmin) and the thermodynamic priors (Tmin. steady-state gain threshold a) (see Appendix B for construction details).
Closed-form solution of the ODE. Substituting Eq. into Eq. 5 and evaluating the kernel integrals term by term (see Appendix A for the detailed derivation), we obtain closed-form expression for the temperature of each thermal Gaussian at arbitrary time t:
T1(1)= Tony + (Ti,
Tanv) t//r
+
C1(1 + (WHT,)?]
Ti
An, [ssn(wwss)) wiTH cos(wrl) + wots e t//r)
(8)
k=1
+ Bi, (cos(wret) + we sin(wxt) - -e -
3.3 DYNAMIC THERMAL RENDERING
During dynamic thermal rendering, temperatures need be mapped to colors. We adopt a linear model for this mapping. Specifically, we linearly normalize temperatures to grayscale using the temperature bounds measured during acquisition. Let the scene's 's temperature range be [Tmin Tmaxl and the temperature of the i-th thermal Gaussian at time t be (t).. The corresponding grayscale intensity is:
It(t) clip (1(()= Tunin
Tmaz - Tmmnn 0.1).
where clip(- 0, 1) truncates values [0, 1J. During training, we use continuous intensity ((0, 1] interval) to participate in differentiable loss, and then map it to pseudo color during visualization to enhance the visual effect.
For rendering, we perform standard alpha compositing along each ray while keeping the usual trans- mittance Tr; and opacity as, but use (t) instead of the SH color term of 3DGS. The dynamic thermal rendering follows the equation below:
N
C= (t).
(10)
3.4 TRAINING AND OPTIMIZATION
Our overall training and optimization framework follows the traditional 3DGS optimization process, using the difference between the rendered image and the ground-truth image to drive gradient back- propagation, thereby continuously updating the geometric and thermal properties of the Gaussians. Based on the original 3DGS loss function, we introduce an additional regularization constraint based on the characteristics of dynamic thermal scenarios to stabilize the learning of the heat source har- monic parameters Ai,k and B, to prevent overfitting and oscillation. The final total loss function is:
Liotal = (1 A) L1 + ALD-SSIM + Areg Σ (A + B,A)),
(11)
t.k
Where C1 and CD-SSIM are widely used in Verf/3DDS-styll reconstruction (Kerbl et al. (2023)), their specific definitions can be found in Appendix E. This loss design allows method to preserve rendering accuracy while mitigating overfitting in thermal dynamics modeling, thereby ensuring robust convergence even in complex dynamic scenes.
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Visi
Therrnal
5: 1.00
Rod (IKISES)
ieen (IMKSES)
Jesson Orin NX
ee 0.50
Blue (1M05885)
RGB Camera
Glass
RGR Camera
0.00
Wovelenyth Ohm))
Wovellngth Jumi
(b) Spectral response of RGB and IR camemss
IR Camera
Coated Glass
CotteGGia
Cammera
Natural Light
RGB CMOS
Meniter
IR CMOS
(o) Pinet-aligned RGB-IR acquisition platform
Pixelalliged RGB-IR
Figure 3: Pixel-aligned RGB-IR acquisition platform. (a) All devices are mounted on rigid frame to ensure stability. (b) Response bands of the RGB and IR cameras: The RGB camera uses the IMX585 chip (response band 300-800nm), and the IR camera uses an uncooled vanadium oxide (VOx) microbolometer sensor (response band 8- 14m). (c) Optical principle of pixel-level align- ment: A piece of coated glass (coating materials: zinc sulfide, silver) is mounted within the black frame. Visible light passes through the glass and enters the front RGB CMOS, while infrared light reflected by the glass and reaches the side IR CMOS. The two imaging paths share the same incident light beam, which split into different wavelengths at the beam splitter.
4 RHD: RAPID HEAT DYNAMICS DATASET
4.1 PIXEL-ALIGNED RGB-IR ACQUISITION PLATFORM.
To efficiently and economically acquire dynamic thermal scene data, we designed and constructed pixel-level aligned RGB-IR acquisition platform, as shown in Fig. 3. The core optomechanical struc- ture consists of piece of selectively coated glass (coating materials: zinc sulfide, silver) positioned at 45-degree angle. Visible light is transmitted to the front-facing RGB camera, while infrared light reflected to the side-facing infrared camera, achieving coaxial imaging and zero-baseline beam splitting. The two images are time-stamped and synchronously captured by the Jetson Orin NX. For calibration and alignment, we first perform intrinsic distortion correction on each camera. We then estimate pixel-level alignment error on common checkboard.
4.2 DATASET CONSTRUCTION.
We introduce a new dataset called Rapid Heat Dynamics (RHD), acquired using the pixel-aligned RGB-IR acquisition platform described in section 4.1. The basic specifications of the RHD dataset include: 512x410 resolution, 10 dynamic thermal scenes, and a total of 2363 views. The RHD dataset covers dynamic thermal scenes with rapid temperature changes associated with typical ther- modynamic processes, such as cooling, warming, heating, and heat transfer; covers a variety of materials, including metals, fabrics, and organic materials; and covers temperatures ranging from low to high temperatures (-1.0%C to 101.0%C) It also includes millisecond-accuraal timestamps. For each scene, we provide pixel-level aligned RGB, Thermal (original), and Thermal (pseudo) images, as well as scene metadata (number of views, temperature range, time range, and ambient temper- ature), to facilitate both algorithm use and human interpretation. detailed description of each scene is included in Appendix C. RHD focuses both cross-modal geometric consistency and thermal dynamic richness, providing a high-quality benchmark for subsequent multimodal research, dynamic thermal scene rendering, and physical prior learning.

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Published as a conference paper at ICLR 2026
0.8
Overall Meon Erro:048899
Mean Ervor in Pixels
0.6
0.4
0.2
5
10
20
Images
(a) alignment error per image
(b) defected by RGB camera camera
Figure 4: Alignment Error Verification. (a) Average alignment error for each of 20 RGB-IR image pairs. The overall average error is 0.4869 pixels, reaching sub-pixel accuracy. (b) Comparison of checkboard corner detection results. The RGB camera corners (blue circles) and the camera corners (red crosses) almost coincide.
EXPERIMENTS
5.1 IMPLEMENTATION DETAILS.
We adopt 3DGS as the backbone, with all experimental settings kept consistent with the original 3DGS framework. Models are trained for 30k iterations under the same hyperparameters, with the specific regularization weight set to Areg = 1 x 10 All experiments share the same train/test split, as well as identical initial point clouds and camera poses. We use RGB images to obtain the initial point clouds and camera poses. During training, we use the raw grayscale thermal images as ground truth for differentiable loss computation; for visualization, the grayscale images are mapped to pseudocolor enhance perceptual clarity.
5.2 ALIGNMENT ERROR VERIFICATION
To verify the alignment error of the constructed pixel-aligned RGB-IR acquisition platform, we first perform intrinsic distortion correction on both the RGB and IR cameras. Then estimate the alignment error on a same checkboard. We compare the corner coordinates a #RGB detected by RGB camera with the corner coordinates z detected by the IR camera to accurately calculate the alignment error. The alignment error Eliggn is defined as:
Ealign | TRGBll2
(12)
As shown in Fig. we captured 20 pairs of RGB-IR images for evaluation, with an overall alignment error of 0.4869 pixels, reaching sub-pixel accuracy.
5.3 RESULTS AND EVALUATION
We compare the proposed method with the state-of-the-art static scene reconstruction methods (3DGS, Mip-Splatting and Thermal3D-GS) and dynamic scene reconstruction methods (4DGS and NTR-Gaussian). We quantitatively evaluate the reconstruction quality based three metrics (PSNR (Hore & Ziou (2010)), SSIM (Wang et al. (2004)), LPIPS (Zhang et al. (2018)).
Tab. summarizes the comparison of our method with the five basclines. As can be seen, our ETGS achieves the best results in all metrics, significantly outperforming the existing methods. This im- provement mainly comes from two aspects: First, compared with the static reconstruction baseline, ETGS explicitly introduces the heat exchange process into the model, which can characterize rapid heating/cooling and subtle heat transfer phenomena between objects, which static models cannot do. Second, our closed-form thermodynamic evolution formula can directly calculate the tempera- ture at any time, avoiding the error accumulation and fuzzification caused by numerical integration, thereby maintaining temporal consistency. In comparison with VTR-Gaussing improvement of approximately dB, demonstrating the advantage closed- form thermodynamic modeling in capturing dynamic processes.
achieve PSNR
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Table 1: Quantitative evaluation of our method compared previous work.
Cooling Checkhoard
Warming Bottles
Cooling Dumbhells
Cooling
Cooling Ehike
Heat Transfer
Warning Peaches
Heating Workpieces
Warming
Warming Workpieces
Metric
Method
Avg.
Cups
3DGS
36.27
32.37
29.78
29.74
34.56
39.47
30.48
34.47
24.43
29.94
32.16
Mip-Splattin
36.48
32.44
28.78
29.13
35.16
37.45
32.74
30.06
26.18
26.67
31.51
ThermalBD-GS
39.47
33.61
32.89
32.11
38.77
39.83
34.
34.93
30.96
30.06
34.68
PSNRT
4DGS
33.58
34.50
35.61
33.99
39.75
34.64
30.36
34.15
32.34
33.94
NTR- Gausiann
41.82
34,63
35.18
35.56
38.09
38,
32.44
33.65
28. 18
31.01
34.96
Ours
3DGS
0.978
0.988
0.968
0.960
0,980
0.990
0.987
0,958
0.968
0.974
0.978
Mip-Splatting
0.974
0.988
0.961
0.958
0,980
0.986
0.979
0.972
0,969
0.976
ThermaED-OSS
0.983
0.989
0.981
0.970
0.983
0.990
0.990
0.989
0.978
0.976
0.983
SSIM
4DGS
NTR-Gaussian
0.986
0.987
0.980
0.974
0.974
0.987
0.984
0.982
0.974
0.978
0.981
Ours
0.987
0.992
0.989
0.983
0.985
0.991
0,994
0.990
0.989
0.994
3DGS
0.066
0.087
0.072
0.075
0.031
0.057
0.091
0.031
0.131
0.137
0.078
Mip-Splatting
0.068
0.080
0.093
0.031
0.043
0.126
0,178
0.085
ThermaBD-GS
0.060
0.095
0.050
0.063
0.029
0.062
0.092
0.030
0.110
0.128
0.072
LPIPS
4DGS
0.101
0.075
0.047
0.076
0.065
0.056
0,064
0.073
0.105
0.099
0.076
NTR-Gaussian
0.072
0.092
0.052
0.092
0.098
0.092
0.104
0.055
0.133
0.102
0.089
Ours
0.054
0.072
0.030
0.050
0.028
0.054
0,060
0.028
0.085
0.042
0,050
Ground Truth
Ours
3DGS
Mip-Splatting
Thermal3D-OS
4DXS
NTR-Caussia
Figure 5: Comparisons of ours to previous methods. The scenes are, from the top down:Cooling Checkboard, Cooling Bench, Cooling Ebike, Heating Workpieces, Heat Transfer, Warming Bottles, Warming Cups from the RHD dataset.
Fig. 5 shows visual comparison of different methods in typical scenes. It can be observed that the static scene reconstruction methods (3DGS, Mip-Splatting and Thermal3D-Gr exhibit significant temperature deviations. This is because these static methods only learn the average temperature of the scene and cannot obtain accurate temperature values. Dynamic scene reconstruction methods (4DGS and NTR-Gausse Gaussian) exhibit varying degrees of artifacts around the edges of some objects.
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Table 2: Comparisons of training and rendering efficiency of our method with previous methods.
Table 3: Ablation Study. We remove the heat source excitation Q and the regularization term separately to evaluate their impact.
Method
(MB)
(s)
3DGS
2429
166
557
Moml, (MI3)
Timel
Mip-Splatiig
2749
207
589
Method
PSNRT
SSIMT
LPIPS.
FPST
Thermal33 GS
3265
470
4DGS
2290
1159
278
Ours Q
43.70
0.986
0.055
2385
454
NTR-Gaussian
44.99
1469
Ours w/o Regular
42.58
0.982
0.064
2380
187
463
No Regular
Ground Truth
t= 1510
1950
Time(s)
No
1510
1950
Full
Figure 6: Visualization of the ablation study. Left: Ablation of the regularization term. Right: Ablation of the heat source excitation Q.
This is because their implicit modeling of time t makes it difficult to ensure temporal consistency. Our method's explicit modeling avoids this drawback, making the model more closely resemble the actual thermal distribution. We provide detailed visual comparison of all scenes in Appendix F.
Table 4: Ablation Study. Effect of the number of frequencies K on reconstruction quality.
Metric
K=8
K=16
K=24
K=32
K=64
PSNRT 40.57
40.59
40.68
40.77
40.95
SSIMT
0.989
0.989
0.989
0.989
0.990
0.051
Tab. summarizes average gpu memory, training time, and rendering speed over all scenes. Our method trains in 197 s-close to 3DGS and Mip-Splatting and about an order of magnitude faster than 4DGS and NTR-Gaussian- and renders comparably to static baselines while surpassing im- plicit methods. This efficiency follows from combining explicit Gaussians with closed- tem- perature solution, avoiding repeated neural-field evaluations. The Appendix D shows the complete calculation cost for ETGS, static baselines and dynamic baselines.
5.4 ABLATION STUDY
We removed the heat source excitation Q and the regularization term to analyze their roles in the overall framework. Quantitative results shown in Tab. and the visualization results shown in Fig. 6. We evaluated the impact the number of frequencies K in the heat source excitation Q on the reconstruction results, and the results shown in Tab. 4.

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Heat source excitation Q: After removing the heat source term, the model can only rely the exponential decay of Newtomian heat transfer to describe temperature changes, resulting in a lack of external driving force for scene evolution. In this case, the model often fails to capture complex temperature variations or periodic fluctuations, and the learned temperature field exhibits underfit- ting. As shown on the right side of Fig. 6, after removing Q, the model misses fine details and edges in the scene.
Regularization term: The regularization term that we introduced constrains the parameters A and B of the frequency basis expansion to prevent them from uncontrolled amplification. After removing this term, although the model still fits the overall trend, unphysical oscillations occur over long time series. This causes the temperature evolution curve to deviate from the smooth physical law, introducing noticeable fluctuation artifacts in the rendering (Fig. 6, left).
Number of frequencies K; As the number of frequencies K' increases, performance improves slightly, but the improvement quickly saturates. Even smaller K (e.g., 8-16) are sufficient to capture the main frequencies, while K 24 strikes a good balance between accuracy and computational cost. Therefore, we used this value our main experiments. Increasing K above 32 yields very slight improvements (PSNR < 0.2 dB, SSIM and LPIPS remain almost unchanged).
DISCUSSION
Independent and Coupled Modeling of Gaussians. Although ETGS models the thermodynamic evolution of each Gaussian as an independent thermodynamic process, the rendered thermal field not independent between different Gaussians, but rather implicitly coupled. This naturally stems from two mechanisms:(1) overlapping Gaussians. Adjacent Gaussians contribute to the same pix- els the rendered image. Any temperature discontinuity between adjacent Gaussian bodies im- mediately produces visible artifacts. (2) dense supervision. Infrared images provide hundreds of thousands of constraints for each view. During optimization, the renderer forces Gaussians lo- cal regions to match the same pixel observations, which implicitly achieves smooth temperature changes between adjacent Gaussians. Explicitly modeling heat conduction between Gaussians is an interesting direction for future research. However, it introduces enormous computational and implementation complexity: global coupling between hundreds of thousands of Gaussians, the in- ability to obtain closed-form solutions, and significantly increased backpropagation costs. ETGS focuses on lightweight, closed-form solutions that are physically accurate and capture the main ther- modynamies we observe in controlled dynamic scenes, while also extending explicit inter- Gaussian conduction as an important feature research direction.
More complex thermodyne namic models. ETGS adopts first-order linear heat-transfer model con- sisting of Newtonian cooling and harmonic heat-source excitation. This formulation is intentionally chosen because it admits a closed-form analytical solution, enables efficient optimization compa- rable to static 3DGS. However, real-world thermodynamic processes may involve nonlinear effects such as temperature--deeeddent conductivity, radiation coupling, multi-layer material interfaces, or even phase transitions. These phenomena are difficult to incorporate into closed-fore solution, and typically require solving nonlinear PDEs or numerical approximations, which would significantly increase computational cost and compromise the efficiency advantage of explicit Gaussian splatting. Extending ETGS to support nonlinear or higher-order thermal dynamics is an important direction. Developing such models would allow ETGS to generalize more complex thermal scenarios, in- cluding outdoor environments, heterogeneous materials, or strong radiative interactions.
7 CONCLUSION
ETGS embeds thermophysics into explicit Gaussians and derives closed-form temperature solution for efficient, stable dynamic thermal reconstruction. We also release RHD with pixel-aligned RGB- IR and ms-level timing. In future work, plan to expand RHD include moving heat sources and more complex environments. Combining RGB with thermal supervision is also a very promising direction to explore.
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ACKNOWLEDGMENTS
This work was supported in part by the National Natural Science Foundation of China under Grant 62372235, Grant 62406069, in part by the China Postdoctoral Science Foundation, under Grant 2024M750425.
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APPENDIX
We organize the appendix as follows:
Appendix A: A complete derivation of the thermodynamic evolution of thermal Gaussians is given (starting from Newtonian heat transfer, obtaining an analytical solution via the integrating factor method, and deriving closed-form differentiable expression at any time under a harmonic heat source).
Appendix B: Detailed description of the construction principles and implementation of the frequency grid, the determination of upper and lower bounds for sampling and thermal prior constraints, logarithmic sampling and minimum frequency separation, and engineer- ing treatment for robustness.
Appendix C: Report on the scene and time statistics, temperature range, and metadata of the RHD dataset to support reproduction and benchmarking.
Appendix D: The complete calculation cost for ETGS, static baselines and dynamic base- lines.
Appendix E: Details about the definitions of common loss functions.
Appendix F: complete visual comparison of each scene (including local zoom) is pro- vided as an intuitive supplement to the quantitative indicators in the main paper.
Appendix G: Outlook for the potential expansion of the method towards more complex thermal processes and multimodal fusion.
Appendix H: The Use of Large Language Models (LLMss.
A COMPLETE DERIVATION OF THERMODYNAMIC EVOLUTION
Linearization and Integrating Factor: Rewrite Eq. 3 into standard linear form:
df; 1 -T. 1 Ton C, -.10).
(13)
di
T
Let the integrating factor be v(t) = el/ri, Multiplying both sides of the equation by s(t) and then differentiating, obtain:
d
(d)TT((())= = Tem et/n
ct)
(14)
dt
C
Integrating overt E [0, t] and denoting the initial condition T,(0) = Tr.u- then obtain:
1 Tem (' e/ ds I { cl
e/TTT(t)) T =
(15)
where multiplying both sides by -t/r, gives:
1 I' ((t=s)/m
Ti(1) Tem + (Ti,0 Tew) e t// + C.lo
(16)
Eq. 16 is the as Eq. 5 in the main text.
Heat source and kernel convolution: Eq. 6 in the main text given as:
K
Q1(t) = Σ
(Aussin (wat) + Bi, (wat)).
(17)
k=1
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Two types of kernel convolutions need to be evaluated:
Liin (w, 1) = (-- e-(1-o)/ sin (ws) ds,
(18)
Loss (w, 1) = /" 6 (t(sss)/ cos (ws) ds.
(19)
Let 1/T, and = w. Using the indefinite integral identities:
/ e sin (bs) ds
(asin bs boos bs),
(20)
a² + b
/ e eeccos cos (bs) ds
eas a² 122
(acos bs + bsin bs).
(21)
Using (t-s)/r: t/Tig//1 simplify, we obtain the following definite integrals:
1
1 Sin wt woos wt + we we-t/ri
Lsin (w,t) = a² + 62
(22)
Leos (w,
coswt wt + wsin wt -t/r/)
(23)
a + 12
1+ ?
Substituting = 1/T, and using a² b²
yields the compact forms:
Ioin (w,,) 1 + w2
sin wT.coswt WT 1/1).
(24)
Icos (w,t)
coswl + wr,sin wl - e et//7)
(25)
1 + 2
Substituting Eq. 24 and Eq. 25 into the convolution term of Eq. 16, we obtain the final closed-form solution:
T1(1)= Tany + (Ti,o
TTav) t//
K
C²(1 + (w)rs)3) { (a.x[sin(we)) WiTh cos(wut) + tWTTe e(mi)
Ti
+
(26)
k=
+ Bi [cos(wxet) + wen sin(wxl) - -in(wat))e--1/11 -//1/
which corresponds to Eq. the main text.
B FREQUENCY BOUNDS: JOINT CONSTRAINTS FROM SAMPLING AND THERMODYNAMICS
We expand the heat source Qt(t) log-uniform frequency grid, whose passband [Wmin Wmax determined jointly by the observation duration and sampling rate sioocssprocessingg perspective) and thermodynamic time-constant priors (physical perspective), balancing expressiveness and bustness. The initial number of frequencies is set to = 24, and is finally adapted to the number of deduplicated active frequencies, i..., K [wx H--
Lowest frequency fuin: Determined by the observation duration. finite observation duration T spon sets the minimum resolvable frequency grid A xe 1/Tspan- In other words, if frequency
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lower than spTapan= full cycle cannot fit within the window and is indistinguishable from lower components. Hence we set:
min max
T Tspan 10 10
(27)
Sampling upper bound Ingei Constrained by the Nyquist frequency (Shannon (2006)). For nonuniform timestamps with minimum interval dtmin- we define an effective maximum sampling rate fmar 1/dtmin which yields a strict unti-aliasing bound:
Fmaax
fayg
(28)
2
2d1min
Thermodynamic, upper bound fix: Given by the first-order thermal inertia low-pass charac- teristic. Model each thermal Gaussian as a first-order linear thermal system with time constant Ti. Its steady-state implitude-frqquene response to the angular frequency w is:
IG (jw))
(T> 0)
(29)
V (WT)2
When the frequency increases, the system exhibits a low-pass characteristic and decays at 1/w. We require that the system can observe the heat source at the candidate frequency (the steady-state gain less than the threshold a e (0, 1), then
G (jww] a,
(30)
equals
(31)
a
The corresponding upper limit of the frequency is
1 a 1,0 1,0)
fer 2TTmin
max
(32)
where we use the fastest thermal time constant prior Twin (i.e., the "minimum thermal inertia" of the material/stmeeture) provide the most permissive physical upper bound. In the special case of choosing the half-power point a 1/v2, the well-known cutoff frequency is obtained as Sc 1/(2TT). Moreover,the time constant satisfies - = C/h, where C the equivalent heat capacity and h the heat transfer coefficient in Newton's 's law of cooling. The exponential decay solution in the time domain and the first-order low-pass behavior in the frequency domain are two consistent characterizations the same thermal process Bergman (2011).
Joint frequency constraints: Combining the sampling and physical constraints, the heat source frequency bounds are set
Wmin 2TT fmina
(33)
Wmax = 2n max(min((faqg fea) 1.2 fmin).
(34)
We first take min(fnyq fen) to ensure both sampling safety and thermodynamic responsiveness. Then compare this value against 1.2 fmin to guarantee nondegenerate bandwidth-i.e., even under extremely sparse short observation windows, the usable band remains at least one frequency-bin wide. This prevents the collapse of the upper and lower bounds to the same point, which would invalidate log-spaced sampling of the frequency grid.
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C RHD: RAPID HEAT DYNAMICS DATASET
As summarized Tab. 5 and Tab. 6, we present our RHD dataset. Built with pixel-aligned RGB- IR acquisition platform of Section 4.1, RHD has resolution of 512x410, comprises 10 dynamic thermal scenes, and totals 2363 viewpoints with millisecond-accurate timestamps. RHD covers canonical thermodynamic processes-cooling. warming, heating, and heat transfer-and spans diverse materials including metals, fabrics, complex devices, and organic objects, with temperature range of -1.0 ²C to 101.0 OC For each scene, provide pixel-aligned RGB, Thermal (raw radiometric grayscale), Thermal (pseudocolor), and scene metadata (number of views, lemperature range, time span, ambient temperature). With its rich cross-modal and thermal dynamies content, RHD as a high-quality benchmark for multimodal 3D reconstruction, dynamic thermal scene rendering, and learning with physical priors.
Table 5: Each scene of the Rapid Heat Dynamics Dataset.
Thermaloriginal)
Thermakpseuddo)
Views
Temp. Range (*C)
Time Range
Eav.
Temp
Cooling Checkboard
218
2145.488
26.5
72.0
Cooling Dumbbells
210
28.0
2115.472
32,3
46.0
Cooling Bench
22.1
31.0
1689.206
32.9
56.0
Cooling Fbiie
315
26.0
1954.054
30.2
60.0
Heal Transfer
21.0
1730.072
41.0
Heating Workpieces
12.0
1249.084
101.0
Warming Bottles
209
3988.082
26.6
31.0
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Table Each scene of the Rapid Heat Dynamics dataset.
Temp.
Time Range
Eav.
Scene
RGB
Thermal(origial)
Thermalpseeudo)
Views
Range (C)
Temp
(5)
(C)
Warming
224
-1.0
1678.116
26.9
Cups
30.0
Warming
Peaches
254
30.0
2.0
2284.465
26.9
Warming
3.0-32.0
1584.317
Warkpieces
Table 7: Complete calculation cost.
Cooling Checkhoard
Warming Cooling Cooling Cooling
Heat Transfer
Warming Peaches Workpieces
Heating
Warming Cups
Warming Workpieces
Metric
Method
Bottles
Dumbhells
Bench
Ebike
Avg.
3DGS
2395
2313
2597
2324
2674
2372
2350
2340
2404
2522
2429.10
Mip Splatting
3389
2215
3417
2384
2694
2908
2154
2384
2810
3132
2748.70
Thermal3D.G
3207
3146
3497
3242
3544
3118
2970
3522
3154
3248
3264.80
Mem](MB)
4DGS
2571
1953
3043
1846
3621
1846
1890
2444
1794
1894
2290.20
NTR-Gaussian
4130
4286
4656
ours
2287
2311
2367
2336
2700
2408
2406
2348
2384
2362
2390.90
3DGS
145
177
195
141
166
173
149
160
175
176
165.70
Mip-Splatting
215
205
225
187
207
209
193
215
198
2.17
207 10
TheralBD-GS
527
450
522
470.40
T(8)n
4DGS
791
847
905
1603
1521
16:37
1621
1054
798
814
1159.11 10
1358
ours
129
203
279
185
188
188
205
208
186
199
197.00
3DGS
537
550
422
584
562
602
613
544
S81
575
557.00
Mip-Splattin
630
648
132
606
658
633
643
613
671
652
588 60
ThermalD-GS
344
305
351
356
352
312
349
357
341,90
FPST
4DGS
284
274
279
284
279
278
283
251
287
281
278 00
NTR-Gaussian
77
83
65
67.70
486
442
396
458
449
487
477
421
478
489
458.30
D COMPLETE CALCULATION COST
Tab. provides complete comparison of training memory, training time, and rendering FPS across all ten scenes in RHD. ETGS achieves a highly competitive computational profile. In terms of train- ing memory, ETGS requires 2390 MB on average, which significantly lower than Thermal3D-GS (3265 MB), and dramatically lower than NTR-Gaussie (4439 MB). This demonstrates that the ex- plicit thermodynamm modeling introduces minimal memory overhead compared with static 3DGS, and is far more memory-effciiett than dynamic baselines. In terms of training time, ETGS trains in 197 seconds average, which is much faster than all dynamic baselines (e.g., 4DGS: 11599 s, NTR- Gaussian: 1469 s), and slightly slower than static 3DGS (166 s). In terms of rendering speed, ETGS achieves 458 FPS, which is very close to 3DGS (557 FPS), and far above all dynamic NeRF/3DGS methods. This confirms that the closed-for foorffommm temperature solution introduces no runtime bottle- neck, preserving the hallmark real-time rendering performance of 3DGS. Overall, ETGS maintains the computational efficiency of static 3D Gaussian Splatting while providing physically grounded dynamic thermal modeling.
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E
DEFINITIONS OF COMMON Loss FUNCTIONS
Photometric Loss Li:
C1 Feenereed -ggll1
(35)
Where fendered represents the rendered image and Let represents the ground truth image. This pixel-wise L1 loss is the standard reconstruction objective used in NeRF/3DGS-stye optimization.
D-SSIM (Structural Dissimilarity) Loss:
SSIM (frendered Lgs)
P
(36)
2
Where SSIM represents Structural Similarity Index, which is used to measure the similarity be- tween two images in terms of structure, brightness, and contrast (Wang et al. (2004)).
F COMPLETE VISUAL COMPARISON RESULTS
Fig. shows visual comparison of all scenes from the RHD dataset. This overall comparison demonstrates the advantages of ETGS in detail fidelity and temporal consistency. 3DGS, Mip- Splatting, and Thermal3D-Gr are relatively stable terms of structural preservation, but they lack the detail and dynamic consistency of temperature gradients, making them unable to reproduce time- varying thermal processes. 4DGS and implicit modeling makes it difficult to ensure temporal consistency. Our method maintains sharper edges, more reasonable temperature gradients, and dynamic evolution consistent with the actual thermal distribution in all scenes.
attempt to model the time dimension, but their
G FUTURE WORK
While ETGS has made significant progress in dynamic thermal scene reconstruction, several areas remain worth exploring.
Extending the RHD dataset with more complex thermal processes. While RHD provides millisecond-level RGB-IR observations for wide variety of thermal processes, future versions of the dataset will incorporate moving or time-varying heat sources, stronger environmental distur- bances, and more diverse materials. These additions will enable evaluating thermal reconstruction methods under significantly more challenging real-world conditions.
Coupled RGB-IR modeling. natural extension of ETGS to integrate a physically in- formed RGB renderer to jointly model appearance and temperature. Such coupled model could optical effects, including glowing surfaces or emissive materials high temperatures, appearance changes due to radiative transfer, refraction, thermal reflection, allowing the RGB channel to reflect thermal variations more faithfully. Integrating such cross-modal interactions would enable richer multimodal reconstruction and enhance applications in monitoring. inspection, and simulation.
simulate: cemperature-dependeee
Joint modeling of geometry and temperature evolution. The current ETGS formulation focuses on dynamic thermal processed under fixed geometry. A challenging but exciting direction is to extend ETGS to simultaneously model geometric deformation and temperature evolution, potentially by combining our thermodynamic formulation with deformation fields, dynamic Gaussians, canonical-space warping techniques. This would allow ETGS to handle scenes where both structure and thermal state change over time.
Developing a dynamic thermal reconstruction framework that both interpretable and gener- alizable will be key area of future research.
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Ground Truth
Ours
3DGS
Mip-Splatting
ThermalD-GGS
4DGS
NTR-Gaussian
Figure 7: Comparisons of ours to previous methods all scenes. The scenes are, from the top down:Cooling Checkboard, Cooling Dumbbells, Cooling Bench, Cooling Ebike, Heating Work- pieces, Heat Transfer, Warming Peaches, Warming Workpieces, Warming Bottles, Warming Cups from the RHD dataset.
H THE USE OF LARGE LANGUAGE MODELS (LLMs)
In preparing this manuscript, we employed Large Language Models (LLMs) for language polishing and stylistic refinement, with the goal of improving readability, clarity, and presentation quality.
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Reviews:
[{"review_id": "74ci2x0BE6", "reviewer": "Reviewer_aaeD", "summary": "The paper proposes ETGS, a method for **dynamic thermal scene reconstruction** that embeds explicit thermodynamic modeling into the Gaussian Splatting (3DGS) framework. Instead of relying on numerically integrated ODEs, ETGS introduces closed-form temperature evolution equations derived from thermodynamic principles (Newton’s cooling and harmonic heat source excitation).\nIt also presents a new dataset, RHD (Rapid Heat Dynamics), which includes pixel-aligned RGB–IR image pairs with millisecond timestamps covering heating, cooling, and heat-transfer scenarios. ETGS achieves state-of-the-art reconstruction performance while maintaining efficiency comparable to static 3DGS.", "questions": "Please address my concerns in the weakness part.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The explicit thermodynamic modeling is well-motivated and technically sound, enabling elegant combination with 3DGS.\n2. The proposed method maintains the merits of 3DGS on training and inference speeds by avoiding costly neural integral inference in prior works.\n3. The established RHD dataset is well-designed with pixel-aligned RGB-IR pairs, meaningful for future research.\n4. The comparison experiments are comprehensive, including both static and dynamic baselines.", "weaknesses": "1. The Gaussians are assumed to be independent of each other in the proposed method, which ignores the real-world heat transfer across nearest Gaussians. Therefore, a video or image demonstration of continuity from Gaussian to Gaussian (or part to part) is helpful.\n2. The established dataset (RHD) is relatively small and lacks diversity. Moving heat sources or other factors that influence thermodynamics can be involved to improve the dataset complexity.\n3. What is the performance when combining RGB and thermal supervisions?\n4. The writing of this paper should be improved before acceptance.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "nYlx8FtdKv", "reviewer": "Reviewer_9B6h", "summary": "The paper introduces ETGS (Explicit Thermodynamics Gaussian Splatting), a method for dynamic thermal scene reconstruction that embeds explicit thermodynamic equations into Gaussian Splatting. Each Gaussian incorporates physically interpretable parameters—heat capacity, heat-transfer coefficient, heat source, and temperature—with a closed-form solution to the heat ODE that eliminates numerical integration and enables efficient, stable rendering under irregular sampling. The authors also propose the RHD dataset, featuring pixel-aligned RGB–IR pairs with millisecond timestamps. Experimental results demonstrate strong performance and clear advantages over prior methods.", "questions": "* Could ETGS extend to coupled RGB + thermal rendering where radiance and temperature interact? This coupling seems crucial for realistic multimodal reconstruction and may reveal new advantages of the proposed explicit thermodynamic formulation.\n* How sensitive is the closed-form temperature solution to errors in $\\tau_i$ and $h_i$? Would it remain stable for heterogeneous materials?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* First explicit embedding of thermodynamic laws into Gaussian Splatting.\n* Derivation from heat ODE to closed-form analytical solution with physical interpretation.\n* State-of-the-art metrics.\n* First ms-timestamped RGB-IR benchmark for thermal dynamics.", "weaknesses": "* The framework largely relies on established heat-transfer equations and standard ODE solutions, with novelty mainly in integrating these principles into the Gaussian representation rather than introducing new thermodynamic insights.\n* The framework is demonstrated on controlled thermal scenes; performance in outdoor or multi-object settings remains unclear.\n* Only first-order linear heat transfer is considered; nonlinear effects (e.g., phase change or radiation coupling) are ignored.\n* More analysis on frequency-grid resolution ($K$, $\\omega_{min}$, $\\omega_{max}$) would strengthen robustness claims.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "SxagoStD76", "reviewer": "Reviewer_BcQH", "summary": "This paper proposes ETGS (Explicit Thermodynamics Gaussian Splatting), a method for reconstructing dynamic thermal scenes by integrating physics-based thermal modeling into 3D Gaussian Splatting. The approach extends standard 3D Gaussians with thermal properties: equivalent heat capacity, heat transfer coefficient, and time-evolving temperature. Temperature evolution is modeled via a first-order ODE derived from Newton's cooling law plus a heat source term expanded on a harmonic basis using Fourier features. The authors derive a closed-form analytical solution that enables efficient rendering at arbitrary timestamps without numerical integration. The paper also introduces the Rapid Heat Dynamics (RHD) dataset: 10 scenes with 2,410 pixel-aligned RGB-IR views, millisecond-accurate timestamps, and coverage of canonical thermal processes (cooling, warming, heating, heat transfer). Experiments show substantial improvements over baselines while maintaining training efficiency comparable to static 3DGS.", "questions": "Questions:\n- Why is the PNSR improvement across scenes show such a high variance?\n- What do the learned A_i,k, B_i,k represent physically?\n\nOther comments:\n- Abstract could be written in a less dense way, it lacks conciseness\n- Please fix inconsistent notation (eg G_i)", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper tackles an important and difficult problem at the intersection of computer vision and graphics, with several potential downstream applications.\n- The idea of integrating explicit (albeit simplified) thermodynamical modeling into 3DGS is creative, and addresses a real gap in the literature.\n- The ODE closed-form solution which avoid numerical integration is elegant and principle\n- The model is strongly grounded on physics, enhancing its interpretability\n- The dataset introduced in this paper can be of a significant value to the literature. Its temporal resolution, variety of thermodynamic process and adequate hardware design make it a solid dataset with potential reuse in the field and beyond. \n- The results are strong, with significant improvements compared to baselines, and with a training cost comparable to static 3DGS, which is much faster than dynamical baselines.\n- Evaluation is comprehensive and uses appropriate metrics\n- The paper is generally well written and is easy to follow,", "weaknesses": "- The thermodynamic model presented in the paper is very simplified, missing or oversimplifying important factors like conduction or radiation, non-linear dynamics, and no phase changes. This undermines the \"faithful thermodynamic model\" claim. At best, the model is physically plausible for simplified scenarios. \n- The usage of Fourier Basis for the harmonic expansion requires further justification. While Fourier approximations make sense, it would be benefitial to understand how different alternatives (eg polynomials, splines, or learned basis) would impact the model. The use of K=24 should be ablated.\n- Computational cost should be studied further.\n- The paper misses important technical details, including how and why the hyperparameters were chosen.\n- There is little validation in term of physics plausibility: For example, the learned h for each material (eg fabric or metal), do they match with known material properties? Is energy conservation preserved? Can it extrapolate beyond training time ranges?\n- The dataset has limitations in terms of spatial resolution, and only contains 10 scenes, which limits impact. \n- Evaluation is done exclusively on perceptual metrics, missing the temperature accuracy which I argue is as important for this problem. \n- The paper is not reproducible in its current state (although code was promised). Many hyperparameter values were not reported. \n- Failure cases could be analysed more thoroughly.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "oocV08ke5O", "reviewer": "Reviewer_d4dY", "summary": "This paper proposes ETGS, a novel extension of 3D Gaussian Splatting (3DGS) that enables the reconstruction of dynamic 3D temperature fields from RGB–IR image pairs at arbitrary viewpoints and time instants.\nUnlike conventional 3DGS methods, where each Gaussian stores color information, ETGS instead assigns to each Gaussian a set of parameters that model temporal variations in temperature.\nUsing these parameters together with a Fourier basis representation, the authors derive an ordinary differential equation (ODE) describing the temporal evolution of temperature and show that its solution can be expressed in a closed form (Eq. (8)). Consequently, ETGS can directly estimate the temperature at any given time using Eq. (8).\nThe authors also introduce a new dataset, Rapid Heat Dynamics (RHD), which captures thermal phenomena such as warming, cooling, heating, and heat transfer at millisecond temporal resolution using synchronized RGB and IR cameras.\nExperimental results on the RHD dataset demonstrate that ETGS outperforms existing 3DGS-based temperature reconstruction methods in terms of accuracy, training efficiency, and rendering speed.", "questions": "* In Eq. (2), the term $f_i$ from Eq. (1) is omitted. Would it be possible to extend the model to simultaneously render RGB images by retaining $f_i$? It would be sufficient to mention this as a potential direction for future work.\n\n* Regarding Eq. (11), the definitions of $\\mathcal{L}\\_1$ and $\\mathcal{L}_{D-SSIM}$ should be explicitly stated (for example, in the appendix). At the very least, the references from which these loss terms are derived should be clearly cited in the main text.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "* The paper proposes a natural approach to incorporating physically governed variables into the 3DGS framework.\n\n* The experiments demonstrate that the proposed method can effectively model temperature dynamics without compromising the computational efficiency of 3DGS.", "weaknesses": "* Although the authors provide an aligned RGB–IR dataset, the proposed model appears to rely solely on IR data and does not utilize RGB information. If RGB input is indeed unnecessary for the model, then constructing an aligned RGB–IR dataset may not be essential. In that case, evaluations such as those shown in Figure 4 could potentially be misleading.\n\n* The only dynamic variable in the current formulation is temperature, while the spatial configuration of objects remains fixed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)