유튜브 스트리밍 예정입니다.

1. 일시: 2025년 2월 4일(화), 14:00-16:00

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

3. 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소 / 무료주차는 2시간 지원됩니다.

4. 발표자: 최재영(한국외국어대학교)

5. 주제: Ensemble Deep Network Learning and Its Applications

Ensemble learning is one of the most popular techniques in the area of machine learning (ML) and pattern recognition. In traditional ensemble learning, multiple ML models are constructed and outcomes each coming from individual ML models are optimally combined for the purpose of improving recognition, classification, and prediction performances. In this talk, I explain “ensemble deep network (EDN) learning” that apply ensemble learning techniques to recently developed deep network models, considering the following two important issues: (a) how to construct an optimal set of deep network ensemble with minimum correlation and (b) how to optimally combine deep network ensemble with the goal of obtaining maximum performance improvement. Also, this talk presents how the proposed EDN learning has been used to improve performance in practical applications such as image recognition, fine dust predictions, and time-series data predictions.

1. 일시: 2025년 1월 21일(화), 10:30-12:30

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

3. 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소 / 무료주차는 2시간 지원됩니다.

4. 발표자: 박준서 (고등과학원)

5. 주제: tLaSDI: Thermodynamics-informed latent space dynamics identification

We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

유튜브 스트리밍 예정입니다.

1. 일시: 2025년 1월 16일(목), 10:30-12:30

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

3. 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소 / 무료주차는 2시간 지원됩니다.

4. 발표자: NO ALBERT(연세대학교)

5. 주제: Understanding Memorization in Generative Models via Sharpness in Probability Landscapes

In this talk, we introduce a geometric framework to analyze memorization in diffusion models using the eigenvalues of the Hessian of the log probability density. We propose that memorization arises from isolated points in the learned probability distribution, characterized by sharpness in the probability landscape, as indicated by large negative eigenvalues of the Hessian. Through experiments on various datasets, we demonstrate that these eigenvalues effectively detect and quantify memorization. Our approach provides a clear understanding of memorization in diffusion models and lays the groundwork for developing strategies to ensure secure and reliable generative models

유튜브 스트리밍 예정입니다: https://www.youtube.com/live/2vbdfFuT064

1. 일시: 2024년 11월 14일(목), 14:00-16:00

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 최재성 박사(고등과학원)

4. 주요내용: How reservoir computing differs from conventional neural networks and its potential applications

Reservoir computing emerged as a distinctive paradigm in handling temporal tasks. This framework significantly reduces trainable parameters compared to conventional neural networks while maintaining computational performance. Beyond its initial appeal for efficiency, it has gained attention for its physical implementation and unique applications in nonlinear dynamics-based computing. This presentation explores how reservoir computing opens new possibilities in specialized tasks, including associative memory for dynamics and unsupervised denoising, demonstrating its complementary role to conventional neural networks.

유튜브 스트리밍 예정입니다.

1. 일시: 2024년 10월 30일(수), 14:00-16:00

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 신선영 교수(포항공대)

4. 주요내용: Clustered hidden Markov models

We consider cases where a hidden Markov model (HMM) has so many distinct states that its state space needs a simpler structure. A novel framework we develop, named the clustered hidden Markov model (CHMM), decomposes the state space into sets of clustered states, by adding a hidden process to the HMM. The CHMM consists of two hidden processes and an observable process, where the first hidden process is a Markov process with clustered state representations and the second hidden process has the original state space. The second hidden process is second-order dependent on the first hidden process; that is, the current state of the second hidden process is dependent on the current and previous states of the first hidden process. The CHMM is a new approach to designing the structure of the hidden states while maintaining the information in the HMM. We derive two hidden Markov submodels from the CHMM. The first hidden process and the observable process of the CHMM form a hidden Markov model with additional dependencies while the second hidden process and the observable process of the CHMM form a classical hidden Markov model. A novel finding is that the hidden states corresponding to a clustered state share the same transition probabilities, which are represented as the identical transition matrix rows of the second hidden Markov model. The identical row structure of the transition matrix motivates us to consider the penalization method for learning the CHMM, simultaneously recovering the clustered state space. The penalized estimation maximizes the likelihood regularized by group smooth clipped absolute deviation (SCAD) penalty to all pairwise differences of the transition matrix rows. We establish the asymptotic properties of the penalized estimator. Simulation studies support the outperformance of our proposed method. Its application to protein structure sequence data demonstrates that the CHMM simplifies the classification of protein segments, and consequently improves interpretability.

유튜브 스트리밍 예정입니다.

1. 일시: 2024년 10월 29일(화), 10:30-12:30

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 발표자: 김혜현 교수(경희대학교)

4. 주요내용: Partitioned neural networks for partial differential equations

In this talk, I will give a brief introduction to neural network approximation to partial differential equations (PDEs). To deal with error and performance issues in the neural network approximation, partitioned neural networks (PNNs) can be used as a solution surrogate. PNNs are formed based on the partition of the problem domain and each network in PNNs approximates the PDE solution in each small subdomain. The use of PNNs allows more flexible local network and hyperparameter settings, and more efficient parameter training by parallel computation. In the second part of my talk, I will present iterative algorithms for PNNs, that can utilize the partitioned network structure for the parallel computation. Numerical results will be presented for test examples to show the performance and scalability of the proposed iterative algorithms.

1. 일시: 2024년 8월 29일(목), 14:30-17:30

2. 장소: 판교 테크노밸리 산업수학혁신센터 세미나실

   • 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
   • 무료주차는 2시간 지원됩니다.

3. 14:30-16:00

   • 발표자: 서효원 교수(국립군산대학교)
   • 주제: Multi-agent system on a sphere
   • 초록: As technology advances, multi-agent systems operating throughout the entire Earth’s surface have become feasible. We are concerned with a multi-agent system, which contains centripetal force, inter-particle bonding force, and velocity-alignment operator. In particular, we employ a regularized rotation operator to overcome the singularity problem at antipodal points. In this talk, we introduce several control laws for given tasks, such as target tracking or formation. Using these control laws, we observe the asymptotic behavior of agents: complete or practical synchronization. Our numerical simulations show that it is applicable to reality. The presented results come from a series of work with S.-H. Choi and D. Kwon.

4. 16:00 – 17:30

   • 발표자: 최선호 교수(경희대학교)
   • 주제: MULTI-AGENT SYSTEMS USING BEARING ANGLES AND ANCHOR POINTS
   • 초록: We propose a bearing-based control law for double-integrator multi-agent systems. The objective is that each agent converges towards a predefined point. Since bearing angles alone cannot determine a unique formation, at least three anchor points are required. The leader agents are those converging towards these anchor points. These leader agents have access to the location information of the anchor points, their own location information, and the bearing angles of surrounding agents. We assume that all other agents can only collect bearing angle information from neighboring agents. Like most bearing-based models, our model includes singularities, preventing the use of LaSalle’s invariance principle. To overcome this, we introduce a new energy functional. Using this energy functional and Barbalat’s lemma, we prove that all global solutions of this equation converge to the specified formation.

현장 강의만 진행될 예정입니다.