PhyDAE: Physics-Guided Degradation-Adaptive Experts

• The paper introduces a two-stage cascaded method that converts residual degradation into explicit control signals, enabling stable and efficient expert routing.
• PhyDAE is defined as a physics-guided architecture that couples degradation estimation with specialized module selection across remote sensing and battery applications.
• Empirical results demonstrate improved restoration metrics (PSNR, SSIM, LPIPS) and reduced degradation effects, validating its effectiveness in diverse domains.

Searching arXiv for PhyDAE and closely related physics-guided degradation-adaptive battery methods. Physics-Guided Degradation-Adaptive Experts (PhyDAE) denotes a modeling paradigm in which degradation is elevated from an implicit nuisance factor to an explicit control or routing signal, and expert specialization is constrained by domain physics. In its exact arXiv usage, PhyDAE is the remote sensing image restoration framework introduced in "PhyDAE: Physics-Guided Degradation-Adaptive Experts for All-in-One Remote Sensing Image Restoration" (Dong et al., 9 Oct 2025). In a broader interpretive sense, closely related ideas appear in battery research that couples degradation estimation, physics-guided representation, and adaptive expert or policy selection, including physics-informed reinforcement learning for charging (Padisala et al., 13 Oct 2025), physics-guided test-time adaptation for state-of-health estimation (Feng et al., 2024), and the Physics-Informed Mixture of Experts network for second-life degradation trajectory computation (Huang et al., 21 Jun 2025). This suggests that PhyDAE can be understood both as a specific architecture and as a more general design philosophy spanning restoration, forecasting, and control.

1. Definition and scope

The exact PhyDAE formulation targets all-in-one remote sensing image restoration under multiple heterogeneous degradations, specifically haze, noise, blur, and low-light conditions. Its central claim is that existing all-in-one restoration methods rely excessively on implicit feature representations and lack explicit modeling of degradation physics, whereas PhyDAE transforms degradation information from implicit features into explicit decision signals through a two-stage cascaded architecture, progressive degradation mining, and physics-aware expert modules (Dong et al., 9 Oct 2025).

A broader, inferential use of the term is supported by contemporaneous battery work. The charging framework in "A Physics-Informed Reinforcement Learning Approach for Degradation-Aware Long-Term Charging Optimization in Batteries" does not use the PhyDAE name, but it explicitly estimates Loss of Active Material (LAM) and adapts the CCCV constant-current stage over the battery lifetime, which aligns with the degradation-adaptive, physics-guided aspect of the concept (Padisala et al., 13 Oct 2025). Likewise, the second-life battery paper "Physics-informed mixture of experts network for interpretable battery degradation trajectory computation amid second-life complexities" uses sparse expert routing based on physics-informed signals and is explicitly framed as PhyDAE-style modeling in the supplied material (Huang et al., 21 Jun 2025). By contrast, "Adapting Amidst Degradation: Cross Domain Li-ion Battery Health Estimation via Physics-Guided Test-Time Training" is not a PhyDAE paper, and its physics guidance is described as limited in the supplied text, but it still exemplifies continual adaptation amidst degradation (Feng et al., 2024).

Work	Domain	Degradation-adaptive mechanism
(Dong et al., 9 Oct 2025)	Remote sensing restoration	Residual-guided physics-aware experts with sparse routing
(Padisala et al., 13 Oct 2025)	Battery charging control	LAM estimation and adaptive CCCV constant-current selection
(Huang et al., 21 Jun 2025)	Second-life battery forecasting	Physics-informed mixture of experts plus recurrent trajectory prediction
(Feng et al., 2024)	Battery SOH estimation	Continual test-time adaptation with reconstruction self-supervision

The common thread is not merely the presence of physics priors or experts in isolation. Rather, the defining structure is that degradation is explicitly inferred, represented, and then used to modulate downstream prediction, restoration, or control.

2. Progressive degradation mining and explicit decision signals

In the exact PhyDAE architecture, restoration is organized as a two-stage cascaded design. A first-stage encoder-decoder generates a coarse restoration,

$$\hat{\mathbf{x}}_0 = \mathcal{G}^{(0)}(\mathbf{y}),$$

after which the residual

$\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$

is analyzed rather than discarded (Dong et al., 9 Oct 2025). The second stage refines the result by conditioning on residual-derived degradation cues: $$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$

Two modules are responsible for converting residual evidence into structured guidance. The Residual Manifold Projector (RMP) interprets residuals through manifold geometry, producing multi-scale residual embeddings. The Frequency-Aware Degradation Decomposer (FADD) analyzes residuals in the frequency domain with $7\times7$, $5\times5$, $3\times3$, and $1\times1$ kernels corresponding to low-, mid-, high-frequency, and edge or pixel-wise responses. These signals are fused into a degradation posterior,

$$\boldsymbol{\pi}_{\text{deg}} = \operatorname{Softmax}\left(\operatorname{Linear}\left(\operatorname{Flatten}\left(\operatorname{AdaptivePool}(\mathbf{R}_1)\right)\right)\right),$$

which is a 4-class distribution over haze, noise, low-light, and blur (Dong et al., 9 Oct 2025).

This conversion from residuals to explicit routing signals is the conceptual center of PhyDAE. The paper’s claim is that direct end-to-end restoration is unstable and inefficient when the network must simultaneously identify degradation type, estimate severity, and reconstruct the clean scene. Progressive degradation mining separates these functions: coarse correction first, degradation analysis second, expert refinement last. A plausible implication is that this staged factorization is what makes the term “degradation-adaptive” more precise than generic conditional restoration.

3. Expert specialization and sparse routing

PhyDAE’s experts are not generic subnetworks. They are tied to degradation-specific physical models. The dehazing expert is based on atmospheric scattering,

$$\mathbf{I}(\mathbf{p}) = \mathbf{J}(\mathbf{p}) \odot \mathbf{t}(\mathbf{p}) + \mathbf{A} \odot (1-\mathbf{t}(\mathbf{p})),$$

with channel-wise transmittance and mixed global-local atmospheric light estimation. The denoising expert assumes spatially varying noise and uses a three-tier adaptive filtering strategy. The low-light expert is grounded in Retinex-style illumination-reflectance separation. The deblurring expert uses anisotropic Gaussian degradation with directional weighting derived from $\sigma_x$, $\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$0, and $\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$1 (Dong et al., 9 Oct 2025).

Routing is performed by a temperature-controlled sparse activation strategy. Visual, frequency, and degradation-prior cues are fused into logits $\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$2, followed by

$\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$3

and Top-$\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$4 selection,

$\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$5

The paper uses 4 experts and Top-K routing with $\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$6 for efficiency (Dong et al., 9 Oct 2025). Lower $\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$7 sharpens routing, whereas higher $\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$8 softens it.

A structurally analogous but domain-shifted formulation appears in PIMOE for second-life batteries. Its Adaptive Multi-degradation Prediction (AMDP) module defines the latent degradation trend as

$\mathbf{r}_0 = \mathbf{y} - \hat{\mathbf{x}}_0$9

where routing weights are produced by a noisy sparse gate,

$$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$0

That model uses 5 experts with TopK = 2, and regularizes batch-averaged expert usage through

$$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$1

to prevent expert collapse (Huang et al., 21 Jun 2025).

The parallel is exact at the level of mechanism: degradation-sensitive features are transformed into sparse expert allocations. The domains differ sharply, but the architectural logic is shared.

4. Battery realizations of degradation-adaptive physics guidance

In long-term charging optimization, the physics-informed RL framework addresses a specific weakness of the ubiquitous CCCV protocol: the constant-current phase is typically fixed even as degradation accumulates. The charging cycle is modeled as a standard CCCV process from $$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$2 to $$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$3, ending when the CV current falls to 0.1 A. Each RL step corresponds to one full charge cycle, and the controller chooses the magnitude of the constant-current part of CCCV for the next cycle (Padisala et al., 13 Oct 2025).

The method uses PyBaMM as the battery “truth model,” Stable-Baselines3 for implementation, and a PPO agent. The environment is based on the Doyle-Fuller-Newman (DFN) model, while the reward includes a reduced-order Single Particle Model (SPM) reference voltage. The RL state is

$$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$4

and the action is

$$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$5

so the agent both adjusts the next-cycle CC rate and updates an internal estimate of the cathode active material volume fraction $$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$6, which represents LAM. The reward is

$$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$7

with a degradation safeguard penalty of 500 when

$$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$8

Episodes are trained over 100 cycles (Padisala et al., 13 Oct 2025).

PIMOE addresses a different battery problem: computing degradation trajectories for retired cells under second-life uncertainty from single-cycle partial data. It uses a partial charging curve from a random initial SOC to cutoff voltage, a 30-minute relaxation voltage curve, and future operation inputs consisting of charge current, discharge current, temperature. From these signals it extracts 12 normalized features—6 from relaxation voltage and 6 from capacity-voltage curves—including the specially designed $$\hat{\mathbf{x}} = \mathcal{G}^{(1)}\left(\mathbf{y}\mid \mathcal{M}_{\mathrm{RMP}}(\mathbf{r}_0), \mathcal{F}_{\mathrm{FADD}}(\mathbf{r}_0), \boldsymbol{\pi}_{\mathrm{deg}}\right).$$9 and $7\times7$0, then feeds the latent trend embedding into the Future-Operation Recurrent Neural Network (FORNN) for long-horizon trajectory prediction (Huang et al., 21 Jun 2025).

BatteryTTT occupies a third position. It is a two-head Y-shaped architecture with shared feature extractor $7\times7$1, regression head $7\times7$2, and self-supervised head $7\times7$3. The adaptation pipeline has joint pre-training, fine-tuning using the first cycle with SOH $7\times7$4, and self-supervised test-time training in which each new unlabeled sample updates $7\times7$5 and $7\times7$6 while $7\times7$7 remains frozen. The supplied text explicitly notes that this paper does not contain rich physics-guided battery constraints such as monotonic capacity fade or conservation-law regularizers; its adaptation signal is instead a reconstruction loss on charging curves (Feng et al., 2024). This makes it adjacent to PhyDAE in degradation adaptivity, but not identical in its use of physics.

5. Empirical results and reported operating regimes

The exact PhyDAE paper evaluates on MD-RSID, MD-RRSHID, and MDRS-Landsat. On MD-RSID it reports 26.86 PSNR / 0.9613 SSIM / 0.0586 LPIPS for dehazing, 27.73 / 0.7772 / 0.3221 for deblurring, 32.77 / 0.8862 / 0.2136 for denoising, and 31.96 / 0.9855 / 0.0211 for low-light enhancement. On MD-RRSHID it reports 22.96 / 0.6511 / 0.4423 for dehazing, 33.73 / 0.8787 / 0.2122 for deblurring, 35.17 / 0.9141 / 0.2289 for denoising, and 37.35 / 0.9852 / 0.0442 for low-light. On MDRS-Landsat it reports 39.12 / 0.9928 / 0.0227, 36.88 / 0.8824 / 0.1487, 34.53 / 0.8651 / 0.0991, and 42.24 / 0.9949 / 0.0121 for the same four tasks. The reported model complexity is 17.21M parameters, 65.66 MB memory, and 71.63 GFLOPs, with an average cross-domain retention rate of 76.41% (Dong et al., 9 Oct 2025).

For second-life battery trajectory computation, PIMOE is validated on 207 batteries across 77 use conditions and 67,902 cycles. The abstract reports average MAPE = 0.88% and inference time = 0.43 ms per battery. It further reports 150-cycle forecasts with 1.50% average and 6.26% maximum MAPE, and continued operation with pruned 5 MB training data (Huang et al., 21 Jun 2025).

For degradation-aware charging, the PPO-based method compares three schemes after 100 cycles: proposed physics-informed RL with 8.54% capacity fade, fixed CCCV with 9.61%, and RL without LAM estimate with 10.34%. The reported qualitative behavior is that the learned policy reduces the charging C-rate as the battery aged, which increases charging time somewhat but reduces degradation accumulation (Padisala et al., 13 Oct 2025).

For cross-domain SOH estimation, GPT4Battery reports average MAE = 2.17% in the zero-shot setting, compared with 3.87% for Benchmark1 and 2.97% for Benchmark2, while swarm attains 1.55% under a domain adaptation setting where target data is accessible. The paper also reports 0.87% on SANYO, 0.81% on PANASONIC, 1.43% on CALCE, and 5.56% on KOKAM (Feng et al., 2024).

These results indicate that the PhyDAE pattern is empirically instantiated in at least three forms: restoration quality with efficient sparse experts, history-free degradation trajectory forecasting, and degradation-aware control.

6. Conceptual boundaries, limitations, and common misconceptions

A first misconception is to treat PhyDAE as synonymous with any mixture-of-experts model. The supplied literature does not support that equivalence. In the exact named method, PhyDAE is a remote sensing restoration framework with residual-guided degradation analysis, physics-aware expert modules, and composite losses including DAOT, adaptive pixel loss, expert balance loss, and contrastive loss (Dong et al., 9 Oct 2025). The charging paper, by contrast, is framed as a single PPO-based RL policy rather than an ensemble of experts, and the supplied text explicitly states that it does not use a mixture-of-experts architecture or the PhyDAE name (Padisala et al., 13 Oct 2025).

A second misconception is that “physics-guided” implies fully mechanistic end-to-end modeling. The literature is more heterogeneous. The charging paper anchors learning with DFN and SPM structure and a degradation variable $7\times7$8 representing LAM (Padisala et al., 13 Oct 2025). PIMOE uses physics-informed macroscopic signals such as capacity-voltage and relaxation voltage, but the paper notes that its “physics” is still largely statistical rather than deeply mechanistic (Huang et al., 21 Jun 2025). BatteryTTT goes further in that direction: the supplied text states plainly that it does not provide explicit lithium-ion constraints such as monotonic fade or conservation laws, and instead uses self-supervised reconstruction (Feng et al., 2024).

A third misconception is that degradation adaptivity is automatically comprehensive. In the charging paper, the degradation signal is represented mainly by cathode active material fraction / LAM, so it is not a full multi-degradation expert (Padisala et al., 13 Oct 2025). In PIMOE, future operating conditions are assumed available, and the datasets do not fully cover thermal runaway, internal short circuits, or highly non-stationary and extreme operating environments (Huang et al., 21 Jun 2025). In remote sensing PhyDAE, the reported cross-domain retention rate of 76.41% indicates nontrivial generalization, but not immunity to domain shift (Dong et al., 9 Oct 2025).

Taken together, these limitations clarify the most defensible interpretation of PhyDAE. It is best understood as a structured strategy for combining degradation inference, physics-guided representation, and adaptive specialization. The exact implementation varies from residual-guided sparse experts in image restoration to LAM-aware PPO control and second-life degradation routing in batteries, but the unifying principle is consistent: degradation is explicitly modeled and then used to condition differentiated processing rather than absorbed into a single undifferentiated black box.