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Dandan Chen

Publications and source records attributed to Dandan Chen.

At least 19 recordsLinked to original sources

Robustness of Deep Learning Models for PV Power Forecasting under NWP Forecast Errors: A Spatiotemporal and Physically Interpretable Analysis

Engineering use of AI forecasting models requires not only high nominal accuracy but also predictable behavior under uncertain inputs. In photovoltaic (PV) forecasting, this requirement is especially challenging because numerical weather prediction (NWP) errors are temporally correlated, state dependent, and physically coupled across variables. Existing evaluations, however, often rely on perfect forecast assumptions or simplistic perturbations that do not reflect these characteristics. This study presents a physically constrained robustness evaluation framework based on simulation, using virtual PV power as a controlled response variable to isolate the propagation of input uncertainty from confounders at the plant level. Six representative machine learning and deep sequence models, including PatchTST, GRU, N-HITS, and LightGBM, are evaluated under dynamic NWP perturbations with heteroscedasticity modulated by clear-sky conditions and Erbs reconstruction that preserves radiation consistency. The results show that sequence models provide stronger noise filtering and temporal resilience than a strong tabular baseline under medium to high disturbance regimes. SHapley Additive exPlanations (SHAP) and Integrated Gradients (IG) further support a feature reallocation tendency at the case level, in which predictive reliance shifts from corrupted future forecasts toward more stable historical observations and deterministic physical priors. A Pareto analysis of accuracy under clean conditions, robustness, and computational latency then translates these findings into engineering implications for robustness assessment and model selection under forecast uncertainty.

physics.ao-ph

Physics-Guided Dual Decoding and Spectral Supervision for Global 3D Hydrometeor Prediction

While global data-driven models excel at predicting continuous atmospheric variables, three-dimensional hydrometeor forecasting remains challenging due to the zero-inflated, long-tailed distributions of these variables. Standard deep learning optimization often yields overly smooth forecasts, attenuating extreme events and spatial textures. We propose PredHydro-Net, a physics-guided dual-decoding framework that mitigates this smoothing. To resolve multi-variable optimization conflicts, it employs a decoupled architecture where macroscopic thermodynamic and dynamic fields unidirectionally modulate hydrometeor generation. By integrating wavelet-based frequency decoupling, spectral amplitude matching, and adversarial training, the model achieves a favorable trade-off between quantitative accuracy and spatial fidelity. In a 72-h global evaluation, PredHydro-Net outperforms both spatiotemporal deep learning baselines (Earthformer and PredRNNv2) and the operational Global Forecast System (GFS) in extreme-event detection and spectral representation. Furthermore, it demonstrates strong climatological consistency with Global Precipitation Measurement (GPM) satellite retrievals. The model reasonably reproduces the three-dimensional cloud structures in extreme weather events, such as Hurricane Ian. Feature attribution confirms its dependence on physical precursors such as relative humidity and wind convergence, offering a robust, physics-informed approach to long-tailed atmospheric prediction.

cs.LG

MAG-Net: Physics-Aware Multi-Modal Fusion of Geostationary Satellite and Radar for Severe Convective Precipitation Nowcasting

Radar-based convective precipitation nowcasting suffers from rapid performance degradation beyond 30 minutes due to missing thermodynamic variables. Existing deep learning models also face blurring effects, training instability, and limited interpretability. To address this, we propose MAG-Net, a Physics-Aware Multi-modal Attention-guided Generator Network. It integrates radar dynamics with selected geostationary satellite channels (IR 10.8, WV 7.1, BTD) to incorporate thermodynamic and microphysical precursors. MAG-Net features a Dual-Stream Encoder for heterogeneous modalities and a Symmetric Dual-Head Decoder optimizing reflectivity regression and event probability via an uncertainty-weighted multi-task strategy. Furthermore, an inference-time Gradient-Preserving Fusion (GPF) strategy combines probabilistic constraints with regression details for better high-frequency texture retention. Experiments on a large-scale dataset (2018-2023) over southeastern China show MAG-Net outperforms deterministic (e.g., CPrecNet) and generative (e.g., DGMR) baselines. Specifically, it improves CSI40 by 0.083 (0.172 to 0.255) over CPrecNet, enhancing intense convective echo detection. Finally, Integrated Gradients (IG) analysis reveals the model's reliance on satellite inputs increases with forecast lead time and convective intensity, confirming that satellite data captures critical precursors for severe weather prediction.

physics.ao-ph

Congruences Modulo Powers of 7 for the Reciprocal Crank Parity Function

Amdeberhan and Merca recently studied arithmetic properties of the sequence $a(n)$, the reciprocal of the crank parity function, which counts the number of integer partitions of weight $n$ whose even parts are monochromatic and whose odd parts may appear in one of three colors (OEIS A298311). A key result of their work was the congruence $a(7n + 2) \equiv 0 \pmod{7}$ for all $n \geq 0$. We prove new congruences for the reciprocal crank parity function modulo powers of $7$.

math.CO

A generalization of the Mordell integral

We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.

math.NT

Congruences modulo powers of $3$ for generalized Frobenius partitions $C\Psi_{6,0}$

In 1984, Andrews introduced the family of partition functions \(c\phi_k(n)\), which counts the number of generalized Frobenius partitions of \(n\) with \(k\) colors. In previous work, we proved a conjecture on congruences for \(c\phi_6(n)\) modulo powers of 3. In this paper, we consider the \((6,0)\)-colored Frobenius partition functions \(c\psi_{6,0}(n)\). We establish a connection between the generating functions of \(c\psi_{6,3}(n)\) and \(c\psi_{6,0}(n)\) via an Atkin-Lehner involution, and prove congruences modulo powers of 3 for \(c\psi_{6,0}(n)\).

math.CO

On Bilateral Multiple Sums and Rogers-Ramanujan Type Identities

We establish some new bilateral double-sum Rogers-Ramanujan identities involving parameters. As applications, these identities yield several new multi-sum Rogers-Ramanujan type identities. Our proofs utilize the theory of basic hypergeometric series in conjunction with the integral method.

math.CO

Combinatorial Proofs for Overpartitions and Two-Colored Partitions II

Andrews and El Bachraoui recently studied various two-colored integer partitions, including those related to two-colored partitions into distinct parts with constraints and overpartitions. Their work raised questions about the existence of combinatorial proofs for these results, which were partially addressed by the first author and Zou. This paper provides combinatorial proofs for the remaining results concerning two-colored partitions and overpartitions with constraints.

math.CO

Congruences modulo powers of $7$ for $k$-elongated plane partitions

The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. Congruences for $d_k(n)$ modulo certain powers of primes have been proven via elementary means and modular forms by many authors. Recently, Banerjee and Smoot established an infinite family of congruences for $d_5(n)$ modulo powers of 5. In this paper we have discovered an infinite congruence family for $d_3(n)$ and $d_5(n)$ modulo powers of 7.

math.NT

Combinatorial proofs for partitions with repeated smallest part

Recently, Andrews and El Bachraoui considered the number of integer partitions whose smallest part is repeated exactly $k$ times and the remaining parts are not repeated. They presented several interesting results and posed questions regarding combinatorial proofs for these identities. In this paper, we establish bijections to provide combinatorial proofs for these results.

math.CO

Congruences modulo powers of $3$ for $6$-colored generalized Frobenius partitions

In $1984$, Andrews introduced the family of partition functions $c\phi_k(n)$, which enumerate generalized Frobenius partitions of $n$ with $k$ colors. In $2016$, Gu, Wang, and Xia established several congruences for $c\phi_6(n)$ and proposed a conjecture concerning congruences modulo powers of $3$ for this function. In this paper, we resolve a revised version of their conjecture by employing an approach analogous to that developed by Banerjee and Smoot.

math.CO

A conjecture of Radu and Sellers on congruences modulo powers of 2 for broken 3-diamond partitions

In 2007, Andrews and Paule introduced the family of functions $\Delta_k(n)$, which enumerate the number of broken $k$-diamond partitions for a fixed positive integer $k$. In 2013, Radu and Sellers completely characterized the parity of $\Delta_3(8n+r)$ for certain values of $r$ and proposed a conjecture on congruences modulo powers of $2$ for broken $3$-diamond partitions. In this paper, we employ an unconventional $U$-sequence to resolve the revised conjecture put forward by Radu and Sellers.

math.CO

On the total number of ones associated with cranks of partitions modulo 11

In 2021, Andrews mentioned that George Beck introduced partition statistics $M_w(r,m,n)$, which denote the total number of ones in the partition of $n$ with crank congruent to $r$ modulo $m$. Recently, a number of congruences and identities involving $M_w(r,m,n)$ for some small $m$ have been developed. We establish the 11-dissection of the generating functions for $M_{\omega}(r,11,n)-M_{\omega}(11-r,11,n)$, where $r=1,2,3,4,5$. In particular, we discover a beautiful identity involving $M_{\omega}(r,11,11n+6)$.

math.CO

Categorical Data Analysis

Categorical data are common in educational and social science research; however, methods for its analysis are generally not covered in introductory statistics courses. This chapter overviews fundamental concepts and methods in categorical data analysis. It describes and illustrates the analysis of contingency tables given different sampling processes and distributions, estimation of probabilities, hypothesis testing, measures of associations, and tests of no association with nominal variables, as well as the test of linear association with ordinal variables. Three data sets illustrate fatal police shootings in the United States, clinical trials of the Moderna vaccine, and responses to General Social Survey questions.

stat.ME

New proofs of theorems on q-orthogonal functions

In this paper, we establish a $q$-integral formula by using the orthogonality relation, and also provide a new proof of the $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials. A new $q$-beta integral with five parameters is evaluated.

math.CA